A. The Mitzvah: 
Setting the table: One is to set his table with a tablecloth, and other normal table settings [such as a lit candle] just like he sets his table for a regular meal. This applies even if one is not currently hungry and only plans to eat a small amount of food, nevertheless he is to set his table as is usually done.
B. The Menu:
One is to wash and eat at least a Kezayis of bread. It is proper to cook meat or another dish in honor of this meal [as opposed to eating mere leftovers]. If one is unable to eat much due to still feeling satiated from the Shabbos meal, he fulfills his obligation even with eating fruits and the like. [Nevertheless if he cannot eat bread he is to initially eat Mezonos bread. If this is not available he is to initially eat another Mezonos food rather than fulfill his meal with fruits and the like. Some say in a time of need, such as if one is unable to eat any food at all, he can fulfill his obligation of Melaveh Malka through having a hot drink such as tea or coffee. If one is unable to eat or drink then he should try to assist others in preparing their Melaveh Malka meal. In any event having a hot drink and bathing in hot water on Motzei Shabbos benefits ones health.  The same applies to eating freshly baked bread on Motzei Shabbos after it has cooled down. Some have the custom to eat garlic during this meal. Some write it is proper to serve fish during this meal.]
Some are accustomed to sing Zemiros and Piyutim after Havdala in order to escort the Shabbos just as is usual to escort the King. [See Q&A regarding the Chabad custom!]
D. Lighting candles:
Some are accustomed to light candles on Motzei Shabbos in order to escort the Shabbos just as is usual to escort the King. [Some are accustomed to light two candles before Havdala. Others are accustomed to light the candles after Havdala. Some light four candles in honor of Melaveh Malka.]
E. Not to do Melacha until after Melaveh Malka:
Some write since the extra soul does not leave until after Melaveh Malka, it is therefore proper to delay doing Melacha which is unconnected to food preparation until after one finishes eating Melaveh Malka. Others write one is not to do any time taking Melacha until this meal. Based on Kabala one is to avoid even learning Torah until this Seuda. [Some suggest to drink something immediately after Havdala and it is hence considered as if he fulfilled Melaveh Malka and he is thus permitted in doing work according to all. Some write it is customary for women to avoid Melacha the entire Motzei Shabbos. This custom was omitted in Admur and is no longer the accepted custom. Some have a custom to avoid writing Safrus on Motzei Shabbos. Others avoid any laborious work done for payment the entire Motzei Shabbos. However according to Admur there is no need to avoid doing so.]
The source behind Melaveh Malka:
The scriptural source for fulfilling the Seuda of Melaveh Malka is in memory of the Man which also fell for the Melaveh Malka meal when the Jews were in the Midbar. The blessing of Shabbos was found in the Man and hence since the Man was also eaten on Motzei Shabbos it comes out that the blessing of Shabbos continues into Motzei Shabbos. This is why it states that the Neshama Yiseira [extra soul] remains until after this meal of Melaveh Malka.
When should one eat the Melaveh Malka?
One should eat the meal as close to the conclusion of Shabbos as possible. Some rule it should be eaten no later than four hours after Shabbos. Others rule it may be eaten until midnight. Others rule it may be eaten any time throughout the night. Others rule it may even be eaten on Sunday or anytime until Tuesday night, so long as he is making the meal in honor of escorting Shabbos.
Are women obligated to eat Melaveh Malka?
If one’s third meal continued until after Shabbos, must he still eat Melaveh Malka?
Some Poskim rule if one ate during the third meal at night after Shabbos exited there is no need to make another meal for Melaveh Malka. Other Poskim argue that one is nevertheless to make a separate meal for Melaveh Malka. Based on Kabala one is obligated to do so.
Is it a Chabad custom to recite the Zemiros or Piyutim for Motzei Shabbos?
Nevertheless some learn these omissions are not because it is not our custom to say it but rather because Admur as a rule did not bring Zemiros, Piyutim, Selichos in the Siddur, being we follow the same Nusach as others in these matters. Nevertheless one is to omit from the Zemiros any versus which mention sadness such as “Yaggon Vaanacha”.
How is one to fulfill Melaveh Malka when Yom Tov falls on Motzei Shabbos?
Some write that one is to add an extra dish of food to the Yom Tov meal in honor of Melaveh Malka.
 This meal is not so much of an obligation but rather a Mitzvah Min Hamuvchar. [300/3] See Lekutei Sichos 36 Beshalach that through fulfilling Melaveh Malka one completes the three Shabbos meals, as Melaveh Malka was instituted in memory of the leftover Man which was eaten on Motzei Shabbos, and only when one eats meals in correspondence to all of the Man are all the meals in full commemoration of the Man. Hence the eating of Melaveh Malka completes the commemoration of the Man which was corresponded to in the eating of the first three meals.
 See Lekutei Sichos 36 Beshalach that this means that the blessing [as opposed to holiness] of Shabbos remains until the end of the meal, and the meal hence serves to escort the holiness of Shabbos.
 M”B 300/3; The Imreiy Eish writes in the name of the Baal Shem Tov that one is to light four candles in honor of the meal
 This ruling of Admur follows the ruling of the Taz 300/1. However the Bach rules “setting the table” means to prepare many dishes of food on the table even just as is done for the Shabbos meals, even if he does not intend to eat more than a Kezayis. [See Lekutei Sichos 36 Beshalach footnote 18; Peri Megadim 300 M”Z 1]
 Or only has a small amount of food left. [ibid]
 See Lekutei Sichos ibid for an analysis on the essence of the Mitzvah of Melaveh Malka. On the one hand it implies from the Gemara and Shulchan Aruch that the main aspect of this meal is not the actual meal but the preparation of the table for the meal, and this preparation is done out of respect for Shabbos, as opposed to Oneg Shabbos, just as is the preparation of the table on Erev Shabbos. Nevertheless from other wordings of Admur it is implied the Seuda itself is part of the Mitzvah and not simply the preparation.
 M”B 300/1; Biur Hagra 300; Machazikei Bracha brought in Shaareiy Teshuvah 300/1; Rav Poalim 3/35; So is also implied from Admur 300/1 that one is to have a Kezayis of bread, and so is the simple meaning of a Seuda and so is the custom. [However see Lekutei Sichos Vol 36 footnote 22 that does not seem to learn this way in the wording of Seuda.] The Gra was very meticulous to eat bread for Melaveh Malka. The Rebbe was particular to wash for Melaveh Malka and to tell Chassidim to do so. However the Ashel Avraham Butchacher [Mahdurah Tinyana 300] writes it is not necessary to push oneself to eat specifically bread.
Lechem Mishneh: Some have a custom to have two loaves of bread [Lechem Mishneh] for Hamotzi, although they only hold one loaf when saying Hamotzi. [Peri Eitz Chaim brought in Kaf Hachaim 300/5; Shlah Hakadosh Shabbos “Neir Mitzvah”]
 The Ashel Avraham [Butchacher Mahdurah Tinyana 300] writes it is not necessary to eat specifically meat and if one desires to eat dairy for whatever reason he may do so and it is considered as significant as meat.
 This is derived from a story in Gemara Shabbos 119 that one is not to suffice with eating leftovers for Melaveh Malka but is rather to cook fresh food for the meal. [Kaf Hachaim 300/8]
 It is not required to eat less on Shabbos in order to have ability to eat a full meal on Motzei Shabbos, as this meal is not a complete obligation, as stated above. [ibid] This ruling of Admur was written regarding the third meal, and placed in parentheses. The Rebbe states the reason for the parentheses is because Admur had doubt as to whether the meal of Melaveh Malka is a separate meal of its own, or a Mitzvah Min Hamuvchar which completes all the other three Shabbos meals. [See Lekutei Sichos Vol. 36 p. 74]
 Shareiy Teshuvah 300/1 in name of Rame, brought in Ketzos Hashulchan 100 footnote 8
 Levushei Serud 300, as is the law by Shalosh Seudos. [ibid] Darkei Chaim Veshalom 473
 Ketzos Hashulchan 100 footnote 8; Minchas Shabbos 96/131 in name of Yaavetz.
 Shaareiy Teshuvah 300/1 in name of Shlah
 Gemara Shabbos 119:
 Gemara Shabbos 119: brought in Kaf Hachaim 300/12
 Baal Shem Tov Al Hatorah Yisro 51; So is an accepted tradition from the Baal Shem Tov and Gr”a. [Piskeiy Teshuvos 300/1]
 Lekutei Mahrich
 See Piskeiy Teshuvos 300/7 for a full list of Zemiros brought in Sefarim
 Luach Dvar Yom Beyomo
 See previous footnotes
 Shaareiy Teshuvah brought in Ketzos Hashulchan 100 footnote 8
Other Opinions: Torah Leshma 79 [of Ben Ish Chaiy] writes there is no Mitzvah or act of piety involved in avoiding work prior to Melaveh Malka.
 Yaavetz, brought in Ketzos Hashulchan ibid
 Peri Eitz Chaim Shaar Hashabbos 24;; Mishnas Chassidim brought in Ketzos Hashulchan 100 footnote 8
 Siddur Yaavetz
 M”A 299/15 in name of Abudarham
 Aruch Hashulchan 299/22
 Based on testimony of Leket Yosher p. 58 in name of Terumos Hadeshen
 Tosefes Shabbos 299/18
 As Admur 299/20 rules that the statement of the Gemara against doing work on Motzei Shabbos applies only until Maariv is finished in Shul.
 See Lekutei Sichos 36 Beshalach in length.
 Chizkuni Beshalach
 Bereishis Raba expounds the verse “Vayivareich Elokim Es Yom Hashevi” that Hashem blessed the Man.
 Ketzos Hashulchan 100 footnote 8
 M”B 300/2 and so is evident from sources above that even Torah should not be learned until the meal commences.
 Yesod Veshoresh Havoda 8/12; Kaf Hachaim Falagi 31/59
 Mishneh Berurah in his understanding of Shaareiy Teshuva 300/1; Ben Ish Chaiy Vayeitzei 23
 Chesed Leavraham brought in Ketzos Hashulchan ibid
 Ashel Avraham Butchacher 174
 Kaf Hachaim 300/2; Peri Megadim 300; Machatzis Hashekel 300
 Kaf Hachaim 300/11
 Elya Raba 300/1 brought in Beir Heiytiv 300/1; Kaf Hachaim ibid; Mishmeres Shalom 29/2; Mentioned in Lekutei Sichos 36 Beshalach footnote 17
 Menorah Hatehorah 300/1; Tehila Ledavid 300/1
 See Igros Kodesh Rebbe Rashab 1 p. 19 that all those Pizmonim which were omitted from the Siddur are not to be recited. At the same time however he also mentions that due to this it was not the custom of the Tzemach Tzedek and his Chassidim to recite Selichos or Avinu Malkeinu on public fast days. Now this has certainly become a fully accepted Chabad custom to do so, despite it not being mentioned in the Siddur, and so on and so forth of other examples of prayers not mentioned in the Siddur which we are nevertheless accustomed to say. [See Kitzur Halachos p. 124]
 Sefer Haminhagim p. 68; Igros Kodesh 13 p. 361
Other Opinions: In Lekutei Torah [Balak] Admur mentions the custom of saying “Al Tirah Avdi Yaakov” on Motzei Shabbos. Some [Ketzos Hashulchan ibid] have concluded from here that it is Admur’s opinion that the Piyut of Al Tirah be sung on Motzei Shabbos. However the Rebbe above says that our custom is not to recite it and the reason it is mentioned in Lekutei Torah is because every custom has a source in Kedusha.
 Shaar Hakolel Hakdama; Ketzos Hashulchan 100 footnote 4
 Ketzos Hashulchan ibid based on Tzemach Tzedek
 Rav Chaim Falagi in Hagada Shel Pesach brought in Piskeiy Teshuvos 300 footnote 10