It is well known that there is a mitzvah to eat the post Shabbos meal, known as the Melava Malka. (Shulchan Aruch 300) Even though many aren’t careful to eat this meal, a Yireh Shamayim (a G-d fearing person) should make an extra effort to keep it. (Aruch Hashulchan 300:3) The midrash says that in the future, a person will be resurrected using a bone located in one’s spine. The meforshim saya that this bone called the luz is fed only with food eaten at a melave malka. (See Mishnah Berurah 300:2) The Mishnah Berurah adds that while this meal may not be obligatory (like the three meals of Shabbos), it is a great mitzvah to eat this meal.
Women are also included in the mitvah of Melava Malka. (See Shemiras Shabbos K’Hilchoso 63:3) Rav Elimelech of Lizhensk zy”a is cited as saying that (for a woman) eating the Melava Malka is a segulah for an easy childbirth. They should even say why they are eating this meal that they are doing so “lshem mitvas Melava Malka” (“for the sake of the Mitzvah of Melava Malka”) (Minchas Shabbos 96 Hasmatos 30)
For this meal, one should eat bread and meat or some other cooked food. If it is difficult to eat bread, he should eat cake or some other mezonos food or at least some fruit. (Mishnah Berurah 300:1) Where this is impossible, one may fulfill his obligation by drinking a cup of coffee or tea. (Shemiras Shabbos K’Hilchoso 63:8)
It is preferred to cook something specifically for Melava Malka and not merely eat leftovers. (Mishnah Berurah ibid. and Shemiras Shabbos K’Hilchoso ibid.)
The The Melava Malka should preferably be eaten soon after the conclusion of Shabbos. If one isn’t hungry one may have it later but shouldn’t do an established activity before having Melveh Malka. The Kaf Hachayim says it should lechatchila be eaten within four halachic hours of Shabbos. The Mishnah Berurah adds that certainly one shouldn’t delay it past midnight (chatzos).
Harav Ovadia Yosef zt”l (Chazon Ovadia Shabbos vol. 2 page 446) adds that if one didn’t do it before chatzos one may still fulfill this mitzvah until Olot HaShachar (dawn). His proof is from a story about the Gra in Tosefet Maaseh Rav (39). One time the Gra was sick on Saturday night and didn’t eat Melava Malka, when he got somewhat better he asked if it was still before dawn since he would still like to eat the Melava Malka. Clearly the Gra held (in case of need) one may eat the Melava Malka until dawn.
The Taamei Haminhagim (page 191, citing the Aishel Avraham of Botchetch) writes that perhaps if one did not eat Melava Malka on Motzei Shabbos, he may still eat it on Sunday as long as his intention is to escort the Shabbos queen. This is also the view of Harav Avigdor Neventzal shlit”a. (Biyitzchak Yikareh on Mishnah Berurah.
There are those who make it a point not to remove their Shabbos clothes until after they have eaten the Melava Malka. (Kaf Hachaim 300:6) The Steipler zt”l, however, felt that one should remove his Shabbos clothes immediately following Havdala, even before Melava Malka. (Orchos Rabbeinu vol. 1 page 107)
Rav Ovadia Yosef zt”l writes that if one’s challah is in the freezer he may remove it on Shabbos in order to thaw out and become edible for the Melava Malka and it is not a problem of Hachana. (Chazon Ovadia Shabbos vol. 2 page 447)
Some have the custom to light candles (without any bracha) in honor of the Melava Malka. (Mishnah Berurah 300:3)