The Rabbinical prohibition- Salting foods:
Meat which has not yet been slated for blood: There is a Rabbinical [prohibition of] tanning food and therefore it is forbidden to salt raw meat, even with intent to eat it raw on Shabbos (if it had still not yet been salted in order to kosher it from its blood).
The reason for this prohibition is: because salt helps raw meat (which has not been previously salted) to soften it and prepare it and make it ready to eat and is [thus] similar to tanning.
Meat which has already been salted for blood: See D below
It is forbidden to salt raw meat even in order to eat the meat on Shabbos, if it had never yet been salted for its blood. Regarding meat that has been previously salted, see next case.
B. Salting in order to preserve/ Pickling foods:
Salting raw meat for preservation: It goes without saying that it is forbidden to salt [meat] in order so it stay preserved and not spoil, even if [not doing so] will cause a great financial loss, and even if it had been already salted and koshered from its blood.
Salting other foods for preservation: This law as well applies for other items [and foods], that it is forbidden to salt them on Shabbos in order to preserve them even in a case of great financial loss.
Pickling foods on Shabbos: Similarly it is forbidden to place heavily salted liquids into vegetables or other foods which are pickled to be preserved (even if one plans to eat from them right away [See Q&A regarding placing cucumbers in salt water] in which case he is not troubling himself for only a weekday purpose) [See Q&A regarding vinegar]
The reason for this is: ([as] nevertheless) since he is pickling them to preserve it is similar to tanning in which the salt preserves them.
Other opinions regarding the reason:  [However] there are opinions which say that pickling is forbidden [not because of the tanning prohibition but] because it is Rabbinically considered cooking.
Summary-Salting a food in order to preserve it:
All foods are forbidden to be salted for preservation purposes, even if not doing so will cause great financial loss.
May one place food in vinegar on Shabbos?
If the vinegar is strong then one may not leave a food in it even for a short time as it appears like one is pickling.
C. Salting foods which salt helps to change their natural state in order to eat on Shabbos:
Regarding placing food in salt water-See 2B! Regarding salting raw meat-See above 2A. The following laws refer placing salt on all other foods.
Not to salt more than one piece at a time: Any item which salt helps to change its natural state, [such as] to soften it or harden it or remove its bitterness and other [changes] of the like, such as for example radish or onion or garlic and the like of other spicy foods which when they are left in salt they secrete and remove their bitterness and become hard, as well as beans and lentils which were cooked with their peel of which salt softens their hardness which they have as a result of their peel [See Q&A], as well as species of raw cucumbers (called ugerkis) of which the salt helps them, as well as all other things which are commonly pickled, it is forbidden to salt more than one piece at a time [even] in order to eat it right away.
The reason for this is because: as when one salts two pieces together and certainly [when he salts] more [than two pieces] it appears like one is pickling pickled foods. [Regarding the reason behind the prohibition of pickling-See Halacha 3A!]
Not to salt for a later use: [Furthermore] even one piece of radish and the like is forbidden to dip into salt and leave it [with the salt] for a long time in order so its sharpness dissipate through it secreting moisture, being that doing so is similar to tanning.
Dipping many pieces individually to eat right away: However it is permitted to dip even a few pieces [when dipping] each one individually and one places it in front of him in order to them eat right away, one after the other without much delay. Even if the [pieces] remain a small amount of time [in their salt prior to being eaten] and they [thus] secrete some moisture [nevertheless] this poses no problem so long as that they do not remain a long time [with their salt] even [when planning to eat them] within the same meal. [Meaning] for example [if] from the beginning of the meal to the end [of the meal there is enough time] for [the salted food] to secrete a lot of moisture [then it is forbidden to delay eating it until the end of the meal] because doing so is similar to tanning which is forbidden [to do] with even only one piece [of food].
[However] there are opinions which say that it is forbidden to leave [the food] in salt at all even for a small amount of time, [and] even [when it is] only a single piece. Therefore [according to this view] it is forbidden to dip two pieces [in salt even] one after the other and then place them in front of him to eat immediately one after the other being that until one [finishes] eating the first piece the second piece remains in the salt. [Thus] it is only permitted to dip a single piece and then eat it right away.
The reason behind why one may not salt more than one piece at a time according to the 2nd opinion: According to the latter opinion the reason that [the Sages] prohibited to salt a few pieces at the same time is not because it appears like [one is] pickling pickled [foods], but rather is because that until one [finishes] eating the first [piece] the second piece remained in the salt and since the salt benefits it, this is similar to tanning. [See Q&A]
Salting many pieces at the same time and then immediately adding vinegar or oil: Therefore [based on the latter opinion] that which [people are] accustomed [on Shabbos] to cut a radish very thin and then place it on a plate and salt it and then pour on it vinegar involves no prohibition even though that this is similar to salting many pieces together which [we said above] is forbidden [to be done] even to eat right away, [as] nevertheless since [the radish pieces] do not remain at all alone with the salt, as one immediately pours on it vinegar and other species, it is [therefore] not similar to tanning. Certainly [this allowance applies] if one pours oil on it being that oil weakens the strength of the salt.  [See Q&A regarding how close to the meal this must be done]
Nevertheless one must beware to pour the oil or vinegar [on the salted pieces] immediately after salting it [and doing so may not be delayed]. However that which some [people] are accustomed to make a vegetable (called lettuce) in which they first salt the vegetable on its own and then leave it this way and drain the water that comes out from it and then [only] afterwards mix it with oil and vinegar, doing so is a complete prohibition and is more similar to tanning [than when it is not left at all alone its salt] being that he delays until [the food] absorbs the salt well. [See Q&A]
The Final Ruling:
The custom is like this latter opinion and so is the law with regards to any [food] which salt benefits. [See Q&A]
Summary- Salting foods which salt helps to change their natural state:
All foods which salt helps to soften it or harden it or remove its bitterness and other changes of the like, which includes all foods which are commonly pickled, may only be salted one piece at a time, and must be eaten immediately. It is thus forbidden to salt another piece prior to eating the first piece as doing so delays the eating of the first piece.
Examples of foods which salt helps change and are included in above restriction: Radishes, Onion, Garlic, Beans and Lentils that were cooked in their peels, cucumbers, lettuce.
Adding oil or vinegar to the food: However if one immediately adds oil or vinegar to the food after salting, [and certainly if one did so even before the salting] then it is permitted to salt even many pieces at the same time [and they may even be eaten later on, on Shabbos, although one must do so in close proximity to the meal.] [See Q&A]
May one place sugar on fruits or vegetables without restriction?
The answer to this is dependent on the disputed reason behind the salting prohibition; whether it is forbidden due to tanning or pickling. However foods that are not normally pickled would be allowed to be sugared according to all.
May one sugar his grapefruit on Shabbos? 
Yes as grapefruit is not commonly pickled.
May one place pepper on foods without restriction? 
Yes as doing so does not involve either pickling or tanning.
May one salt more than one bean at a time and the like of other foods which are usually eaten many at one time?
Yes this may be done according to all, as one does not commonly eat one single bean at a time, but rather many at one time and it thus does not appear like one is tanning/pickling. Although this may only be done to an amount of beans which he will be eating immediately within one mouthful.
It is forbidden to salt more than one mouthful worth of the bean or other food of the like.
If the reason behind the prohibition to salt more than one food at a time is due to that it appears like pickling which itself is prohibited according to some due to that it appears like cooking, why may one therefore not be lenient to salt already cooked foods, after all there is no cooking after cooking?
The reason that this is nevertheless not allowed is possibly because the Sages did not make any differentiation in their decree against salting foods. Alternatively pickling a precooked food is similar to roasting after cooking which is not allowed, as pickling is a different form of cooking than is cooking.
Is the placing of oil and salt in ones food only allowed to be done in proximity to the upcoming meal?
Yes, as this is no different than salting foods which salt only helps to give taste of which is only allowed to be done prior to the current meal and may not be done for the sake of the next meal. [See next Halacha “D” and Q&A there with regards to how close to the meal this must be done!]
Is there any reason to be stringent to first place in the oil and then the salt? 
Yes, as perhaps if one were to place the salt first he may come to forget to place in the oil immediately after. [As well this should be done being that according all opinions when the oil is placed first there is no question of a prohibition, as will be explained in Q&A, and it is better to do an act that will go in accordance to all.]
May one also be lenient like the second opinion, or must one be stringent like both opinions? 
Seemingly the custom is only to be stringent like the second opinion with regards to prohibit the salting of even two foods one after the other. However with regards to leniencies which derive from the view of the second opinion [see the next two questions] seemingly one is to be stringent as holds the first opinion.
May one salt more than one food at a time if he plans to eat both of them at the same time?
Practically although there is certainly room to be lenient, it is proper to be stringent. See footnote below for the reasoning.
May one be lenient to salt many foods and then add oil to it immediately even according to the first opinion, and if not then should one today practically be lenient in the above?
There is room to question whether this would be allowed according to the first opinion. Practically although there is certainly room to be lenient even according to the first opinion, it is proper to be stringent to place in the oil prior to placing in the salt in which case this is permitted according to all without question.
If one salted a food that salt helps change their natural state on Shabbos without adding oil/vinegar to it may one still eat it on Shabbos?
If this was done unintentionally, such as he forgot to place oil in it right away, or he was not aware that salting involves a prohibition, then the food may be eaten. If it was done despite knowledge of the prohibition, and one advertently delayed placing in oil, then it may not be eaten. [See “The laws of Cooking” chapter 2 Q&A there!]
D. Salting foods which salt only helps to give taste:
Any item [or food] which salt does not help to change its nature and rather only gives it taste [See previous Halacha 3C for exact definition], such as for example [ a salted] egg and [pre-salted] meat is [only] forbidden to salt when done in order to leave it for another meal.
Other opinion: [However] there is an opinion which says that if there is any reason that it is better to salt [the food] now as opposed to salting it later on in proximity to the meal, such as if now [the food] is slightly hot and will [thus] absorb the salt much better [if it were to be salted now] then there is no prohibition involved in doing so.
The Final Ruling: (One may rely on their words to be lenient in a [dispute over a] Rabbinical prohibition if one needs to do so).
Summary-Salting foods which salt only helps to give taste:
Is permitted to be done for the need of the coming meal. However for the need of a later meal is forbidden to salt it, unless there is need to do so such as salting it now benefits the food more than salting it prior to the meal.
May one salt his food even much time prior to beginning the upcoming meal?
The Ketzos Hashulchan [based on Magen Avraham] rules that this may not be done. Rather it is only allowed to be salted right before the meal, as is the law with regards to Borer, that it may only be done right before the
Are tomatoes considered foods which salt only helps to give taste?
Yes. Thus it is allowed to be salted without restriction so long as it is done prior to the upcoming meal.
General Summary- The Rabbinical prohibition of Salting:
Salting a food in order to preserve it:
All foods are forbidden to salt in order to preserve, even if not doing so will cause great financial loss.
Salting a food in order to eat on Shabbos:
All foods which salt helps to change their natural state: Such as to soften it or harden it or remove its bitterness and other changes of the like, which includes all foods which are commonly pickled, may only be salted one piece at a time, and must be eaten immediately. It is thus forbidden to salt another piece prior to eating the first piece as doing so delays the eating of the first piece.
Examples of foods which salt helps change and are included in above restriction: Radishes, Onion, Garlic, Beans and Lentils that were cooked in their peels, cucumbers
Adding oil or vinegar to the food: However if one immediately adds oil or vinegar to the food after salting, [and certainly if one did so even before the salting] then it is permitted to salt even many pieces at the same time [and they may even be eaten later on, on Shabbos.]
Meat: It is forbidden to salt raw meat even in order to eat it on Shabbos if it had never yet been salted for its blood. Regarding meat that has been previously salted, see next case.
Salting foods which salt only helps to give taste: Is permitted to be done for the need of the coming meal. However for the need of a later meal it is forbidden to salt it, unless there is need to do so and salting it now is better for the food then salting it only prior to the meal.
Practical questions based on above:
May one place vinegar into his cucumber salad on Shabbos?
See above Halacha 2B Q&A.
May one add salt to his vegetable salad prior to the meal?
If the salad contains cucumbers, lettuce, or onions then this may only be done in close proximity to the meal and only if one has already added oil to the salad or plans to do so immediately after salting it.
May one add salt to his cooked meat or chulent?
Yes, although this may only be done in close proximity to his meal.
May one add salt to a tomato salad?
If the salad also contains onions then it has the same ruling as does a vegetable salad, which requires oil for this to be allowed. If however it is just plain tomatoes, or tomatoes with another vegetable which salt only adds to it taste, then it is allowed to be done close to the meal.
 Otherwise the meat is Muktzah, as will IY”H be explained in the Laws of Muktzah.
 Halacha 2
 This implies that he plans to only eat some of them and leave some more left soaking in the liquid. So is also evident from the reasoning
 Halacha 4
 Ketzos Hashulchan 128 footnote 8
 So rules Rambam
 This is allowed to be done in close proximity to the meal as will be explained in “The laws of Grinding”.
 See story of Chofetz Chaim mentioned in Q&A in the footnote there!
 See Ketzos Hashulchan 128 footnote 2. So rules also Rav SZ”A in SSH”K 11 footnote 1
 According to the second reason mentioned above that salting is prohibited due to a tanning prohibition then sugaring a food would be allowed as it neither serves to soften or to preserve the food, nor is it used in the tanning process.
However according to the first reason mentioned above [the Rambam’s reason] behind the salting prohibition that it is due to pickling, than sugar too would be prohibited to place on foods that are normally pickled, just as is the law with salt, unless it is done in the permitted way mentioned by salt.
 Shabbos Kehalacha Vol. 2 p. 408, Yalkut Yosef
 See Ketzos Hashulchan 128 footnote 2
 Ketzos Hashulchan 128 footnote 2
 Ketzos Hashulchan 128 footnote 2
 [An alternative reason: The second opinion here argues on the fact that salting was prohibited due to pickling and rather holds that it was prohibited due to tanning, and this is the main opinion. As well even regarding the pickling prohibition some hold that it itself is due to a decree against tanning and not because it appears like cooking. Thus the concept of no cooking after cooking is irrelevant according to these opinions and it is thus prohibited to salt a food even if previously cooked. Vetzaruch Iyun as to why the Ketzos Hashulchan ignores this reason and accepts simply that the salting decree is because it appears like cooking.]
 Ketzos Hashulchan 128 footnote 4
 As for the reason that this was not mentioned by Admur, perhaps he relied on the fact that the reader understood that since the case is discussing cutting the radish thin, it can only be discussing a situation that one is doing so prior to the current meal, as otherwise this poses a grinding prohibition, as will be explained in “The laws of Grinding”. [Ketzos Hashulchan 128 footnote 4]
 Ketzos Hashulchan 128 footnote 5
 Ketzos Hashulchan 128 footnote 3
 Ketzos Hashulchan 128 footnote 3
 Certainly this is allowed according to the second opinion mentioned above as is evident from the radish example brought by Admur. However according to the first reason [the Rambam’s reason] there is room to question whether this would be allowed as on the one hand perhaps they view the actual salting of more than one food at a time as appearing like pickling, irrelevant to whether or not one plans to eat them together. However on the other hand perhaps as so long as the salted foods do not delay at all from being eaten, then perhaps even according to the Rambam this would be allowed as it does not appear like pickling.
 Ketzos Hashulchan 128 footnote 3
 As explained in the previous question in the footnote there. To not however that from the wording of Admur above in the radish case it strongly implies that this is only permitted according to the second opinion. On the other hand it is difficult to accept that we would be lenient against the first opinion which is the opinion of the Rambam which is plainly ruled by the Michaber and Rama. It therefore would seem that even according to the Rambam’s opinion this would be allowed, as explained in the previous footnote. Vetzaruch Iyun! [Ketzos Hashulchan 128 footnote 3]
 Ketzos Hashulchan 128 footnote 5
 To note: There is a story noted with the Chofetz Chaim [told over by Rav Shmuel Chaim Kublanken, who was eating by the Chofetz Chaim that Shabbos, to the author of the Ketzos Hashulchan] regarding that he had forgotten and accidently salted radishes prior to adding oil to it [which is possibly forbidden according to the first opinion, as well perhaps he did not have oil] and when he remembered he pushed the radishes away and avoided eating them. Nevertheless one must say that this was a mere stringency of the Chofetz Chaim in order to follow those opinions [Peri Megadim] which are also stringent by Rabbinical prohibitions to forbid the food. This however is not the actual Halachic ruling. As well one must say that the Chofetz Chaim added some liquid to the radishes as otherwise he would in truth have transgressed the salting prohibition according to the second opinion. [Ketzos Hashulchan 128 footnote 5]
 Meaning meat that had been already salted to remove its blood, as otherwise it is forbidden even when done to eat right away as explained in Halacha 2. Vetzaruch Iyun as even pre-salted meat can be salted for preservation and salt helps change its form to harden it, thus perhaps in truth it refers to cooked meat, Vetzaruch Iyun.
 Perhaps Admur mentions only slightly hot as if it were Yad Soledes than it is proper to not place salt on it at all, even in a Keli Sheiyni. [Ketzos Hashulchan 128 footnote 7]
 To Note: The Elyah Rabah rules that it is always permitted to even salt it for the need of the next meal.
 So rules also Mishneh Berurah 21
To Note: From the Ketzos Hashulchan [128/4] it seems that he learned this “need so” to mean that it will soften the meat. However this does not seem to be the simple meaning of Admur, as if so then saying “needs so” is superfluous being that the arguing opinion itself only holds that when one needs so it is allowed.
 Ketzos Hashulchan 128 footnote 9
 See SSH”K 11/2