A. Squeezing Ripe Grapes into food [as opposed to liquid]:
Squeezing grapes directly into food: It is permissible to squeeze a cluster of grapes into a pot of food in order to give better [taste] (see chapter 505 [Halacha 2]) to the food.
The reason for this is: because all liquid that enters into food is considered like food and does not have a status of liquid at all, and thus it is as if one is separating food from food.
Squeezing grapes into an empty bowl and then into food: However if it is not [being currently squeezed into] food then it is forbidden to squeeze it [even if one plans to mix food into it later on].
The Reason: Now, although one plans eventually to mix food into it and it is for this reason that he is now squeezing this wine into [the vessel], in order to use it to enhance and sweeten the food that he will eventually eat with this wine and it is thus liquid which is entered into food which is considered like food, nevertheless since at the time of squeezing the wine there is not yet any food [which is mixing into it] and it is not evident at all that it is for this purpose of enhancing the food [for which he is squeezing the wine], therefore it is Rabbinically forbidden.
Regarding unripe grapes- see D below.
B. Squeezing all other fruits which are edible in their raw state into foods:
- Important note: Regarding the definition of commonly squeezed fruits- See Halacha 2 and Q&A there!
Fruits which are commonly squeezed for Juice: The above law mentioned by grapes applies [as well to] strawberries and pomegranates and other similar fruits that are commonly squeezed for juice when they are in plentiful.
Other fruits which are never commonly squeezed anywhere: However other fruits which are not commonly squeezed for their juice even when there are plentiful of them, then even according to those opinions which forbid to squeeze them for their juices, nevertheless if one is only squeezing them in order to season the food with their liquid then it is allowed even if there is no food currently within the vessel that he is now squeezing them into.
The reason for this is: because at the time of the squeezing it is known to all that he is squeezing them in order to sweeten the food and not in order to drink their juice being that it is not at all common to squeeze these [fruits] for juice.
Apples and lemons: As explained above in Halacha 2C apples and lemons have the same law as fruits which are not commonly squeezed anywhere. Therefore they are allowed to be squeezed according to all opinions for the need of food, meaning in order to flavor the food with their liquids and the like.
C. Squeezing fruits that are not fit to be eaten in their current state, into food:
The above allowance to squeeze fruits in order to season foods is only referring to fruits which are fit to be eaten however fruits which are not fit to be eaten are forbidden to be squeezed according to all opinions even into food.
The reason for this is:  because when one squeezes food which is not fit for eating he is not separating food from food but rather is [separating] food from waste which contains [the prohibition of] “detaching” as was explained in chapter 305 [Halacha 28] and also because of [the prohibition of] separating food from amongst waste even if he wants to eat it right away, as [the Sages] only permitted to separate food from waste with ones hands in order to eat right away because so is the form of eating, to take the food with his hands from the waste and eat it and [it is thus] not similar to [forbidden] work, however to squeeze and then eat is not a form of eating but is a form of work.
Unripe grapes: Likewise it is forbidden to squeeze unripe grapes, which are [all] grapes which have not yet reach the [the size of] a white bean, even into foods because these [grapes] are inedible, and are thus considered like waste in relation to the wine which is squeezed out from it. Now, because we do not know the size of the white bean it is forbidden to squeeze grapes into food until they are fit to be eaten by majority of people.
[However] there is an opinion which permits squeezing unripe grapes into food (and it goes without saying that they permit this to be done to other fruits which are not fit to be eaten, and even to squeeze them for their juice is permitted according to those who permit this with other fruits [which are edible]).
The Final Ruling: 
One is to be stringent like the former opinion. [See Q&A]
D. Squeezing fruits into a liquid:
According to those opinions which forbid to squeeze [any] fruit for the sake of drinking their liquids, then it is forbidden to squeeze on Shabbos lemons or other fruits into water or other liquids in order to drink. [See Q&A]
The Reason: As [the Sages] only said that juices which enter into foods are considered like food [and are thus allowed to be squeezed into them] and not [juices that enter] into liquid.
E. Squeezing into a creamy dip:
It is permitted to squeeze [fruits and pickled foods] into Muryas because it is considered food however into liquids it is forbidden to squeeze them as explained above. [See Q&A]
Summary of squeezing fruits into food and liquid
Fruits that are currently edible:
Directly into food: All fruits, even grapes and olives, are permitted to be squeezed directly into foods.
Into an empty vessel, which will then be poured into food: Is Rabbinically forbidden to be done to all fruits which are commonly squeezed to drink their juice upon having much of them available.
Fruits which are not commonly squeezed to drink their juice even when one has much of them available are permitted according to all opinions to be squeezed into an empty vessel with intent to place into food. [Thus today that almost all fruits have a status that they are squeezed to drink their juice, are forbidden to be squeezed into an empty bowl.]
Directly into Liquids: Has the same laws as one who is squeezing them to drink their juice plain, and thus is only permitted by fruits that are never commonly squeezed for their juice, and only in places that are not accustomed against squeezing these types of fruits for their juice on Shabbos, as explained above in Halacha 2.
A creamy dip: Has the same status as food and not liquid.
Fruits which are not currently edible:
Are forbidden to be squeezed even into food no matter what type of fruit it is.
May one squeeze fruits that are permitted to be squeezed using a juicer?
No. It is only permitted to do so using ones hands, being that using a specified vessel is a mundane act which defiles the sanctity of Shabbos.
How much juice may one squeeze into a food?
One may squeeze as much juice as needed in order to give taste to the dish. However to squeeze more than is needed is only permitted if either a) majority of the juice is being used to give taste to the dish or b) Majority of the juice is not giving taste but majority will become absorbed within the food and thus not be separately recognizable.
Thus it is forbidden to place small amount of food in a bowl and then squeeze into it a large enough amount of juice that the liquid is separately recognizable from the food.
May one squeeze juice onto sugar?
No. This is forbidden with exception to lemon of which in certain cases is allowed- See Q&A below!
May one squeeze lemon into his food?
Yes, as is true of all fruits.
May one squeeze lemon onto sugar?
If one is doing so in order to eat the sugar which has now been saturated with lemon juice, it is allowed. However if one plans to enter the sugar into a drink, then it is forbidden.
May one squeeze lemon into his tea on Shabbos?
The custom today is to forbid squeezing lemon even into a Keli Shelishi, or even into cold tea, as explained in Halacha 2 Q&A that we are today stringent to not squeeze lemons in order to drink their juice. [However according to the Sefaradim this is allowed even today so long as this does not pose a problem of cooking.]
May one cut a lemon over ones tea having its liquid fall into the tea?
May one rub his hands on lemon in order to remove stains from his hands?
May one cut a fruit salad despite the fact that juice will be squeezed in the process, and eventually eaten?
If the juice adds flavor to the fruit salad, as is almost always the case, then it may done.
If it does not add taste to the salad then it may only be done if the juice will get absorbed into the fruit. Otherwise it is forbidden to cut such a fruit on Shabbos with intent to drink its juice.
May one squeeze into food the juice of a peel, such as a lemon peel or orange peel?
Yes, [although it is best to do so only right before the meal in order to avoid the Borer prohibition according to all].
If a food will only become edible due the squeezing may it nevertheless be squeezed?
No, as this contains a Borer prohibition. This may not be done in any case, whether with intent to squeeze the liquid into food or to sweeten it.
May one squeeze juice into a food that also contains liquid, such as gravy or vegetable soup?
By a dish which its main aspect is the solid foods that are in it, such as chicken with gravy or soup with a large amount of vegetables and little liquid: It is allowed if done in order to give taste to the solid.
By a dish which its mains aspect is the liquid, such as a large amount of soup with little vegetables: It is forbidden even if done to give taste to the vegetables.
What is the definition of a liquid? How thin must the fluid be?
If the substance is thick to the point that while drinking it one commonly uses his tongue to help swallow it down then it is defined as a solid and may be squeezed into. If however it is smooth enough to be drunk without help from ones tongue then it has the same status as does liquid and is forbidden to squeeze fruits into it.
May one squeeze juice into a very liquidly dip, such as Italian dressing?
If it is a liquid which is known that is not meant to be drunk but rather to dip bread or other foods into, then it is allowed being that the dip is considered like food. However even in such a case it is only allowed if the liquid was originally a solid and was then squeezed out, as is the case with Italian dressing. However if the dip was always a liquid, such as the water that received taste from a chicken and then became gravy then it is forbidden, as the gravy is viewed as a liquid.
May one squeeze juice into a thick liquidly substance which is not meant for dips, such as fruit or vegetable puree?
This depends on how thick the substance is as was explained in Q&A above- See There!
May one squeeze juice into a melted fatty substance which will eventually congeal?
If one plans to eat the food while it remains a fluid then this is certainly forbidden by those fruits that may not be squeezed to drink their juice. However if one plans to only eat it later after it already congeals then its law requires further analysis.
 There it is explained that squeezing into food is only allowed if the liquid will become completely absorbed into the food. If not then it is forbidden.
 320/9; Rabbeinu Yosef Porat brought in Tur. The first opinions follows the opinion of Rabbeinu Tam.
 The Michaber brings two opinions on this matter regarding inedible grapes, the latter-stringent- opinion being like that of Rabeinu Tam. The Magen Avraham, Tosefes Shabbos, and Mishneh Berurah  all rule like the latter opinion in Michaber, like the ruling here by Admur.
 A creamy dip made from fish fat.
 See 320/2 Q&A 4
 Shabbos Kehalacha Vol. 2 p. 396
 So rules Ketzos Hashulchan 126 footnote 19
 Shabbos Kehalacha Vol. 2 p. 432-433, 439
 So rules Igros Moshe 5/24
 Shabbos Kehalacha Vol. 2 p. 404
 Shabbos Kehalacha Vol. 2 p. 406
 So learns Tzemach Tzedek and so rules Ketzos Hashulchan 126 [footnote 25]. As well so rules: Yabia Omer, Chazon Ish,
However the Radbaz, Mishneh Berurah, Ben Ish Chaiy, Machzikeiy Bracha all rule that it is allowed.
 Shabbos Kehalacha Vol. 2 p. 404
 Shabbos Kehalacha Vol. 2 p. 441
 So rules Yalkut Yosef, based on the Beis Yosef after bringing many proofs that it is allowed.
 Shabbos Kehalacha 7/18
 Shabbos Kehalacha Vol. 2 p. 408
 So rules Teshuvas Lev Chayim,
 So rules Peri Chadash.
However the SS”K 14/17 rules that this too is forbidden.
 Shabbos Kehalacha Vol. 2 p. 444
 So rules Ketzos Hashulchan 126 Footnote 19
 Shabbos Kehalacha Vol. 2 p. 446
 So rules Tehila Ledavid 320/14
 Shabbos Kehalacha Vol. 2 p. 434
 Shabbos Kehalacha Vol. 2 p. 436
 This definition is based on the definition of Admur in the Laws of blessings with regards to when a flour drink becomes Shehakol. [See 208/8]
 Shabbos Kehalacha Vol. 2 p. 434-436
 Shabbos Kehalacha Vol. 2 p. 436
 Shabbos Kehalacha Vol. 2 p. 441
 So rules Ketzos Hashulchan 126 footnote 25