Maran (Rabbi Yosef Karo, author of the Shulhan Aruch) dedicates a full Siman (Orah Haim 300) to the subject of the Melava Malka the Saturday night 4th meal. The reason for this meal is, upon a departure of a king from a town, the people make sure that he is escorted with an entourage. Similarly, when G-d who just spent Shabbat with us leaves, we make a special meal in His honor.
Maran writes that one should set his table on Saturday night in order to escort the Shabbat. One only has to eat a kezayit for this meal. The halachic authorities write that one must show the utmost respect for this meal by making sure there is a table cloth on the table and that the finest cutlery is being used.
The best time to eat this meal is right after Shabbat, if one is unable to have it right after Shabbat he can have this meal until hasot. The Hesed Lealafim (Rav Eliezer Papo 1786-1827) writes that if one is unable to have the Melava Malka meal before hasot, he can eat it until Alot hashahar-daybreak.
Rav Haim Palachi (1788-1869) writes that the extra soul that one received on Shabbat stays with a person until he finishes Melava Malka. With that in mind it is proper to keep the clothing of Shabbat on until after Melava Malka.
One should have new foods that were not eaten on Shabbat by the meal of Melava Malka. One should try to have hot foods and hot drinks at this meal. The Gemara in Masechet Shabbat writes that hot foods and hot drinks on Saturday night bring healing to the body.
