The ShulchanAruch (OC 260:1) paskens, based on the gemara Shabbos (25b), that it is a Mitzva to wash your entire body L'Kavos Shabbos. The Minhag Yisroel Torah 260:1)brings the Zohar which says that RavHamnunaSava would immerse himself in the river every Erev Shabbos in honor of his NeshamaYiseira, in order to receive Shabbos in a state of purity. The SiddurRavShabsai says that Kedushas Shabbos is not evident on a person until he immerses himself in a Mikva. There is a remez in the RosheiTeivos of the pasuk, "Lev TahorBiraElokim". The first letters spell "Taval", immerse in a mikva. Afterwards says the pasuk, V'RuachNachonChadeshBikirbi".
The Arizal was noheg not to dry himself after the Mikva because he wanted the holy waters of Shabbos to seep into his body. The Ben IshChai said that this is not essential, especially if it makes a person uncomfortable. It is enough to leave water on one area ofthe body. The KafHaChaim
writes (260:8) that if you dip more than once then there is no purpose
in leaving the water on your body since the original water is already
gone.
Most people hold that this tevila should be done after Chatzos although the ShaarHaKavanos writes that it should be done an hour before Chatzos.
As for the amount of times you should immerse, there is a range of opinions. The ShaarHaKavanos says twice, once to clean off the weekday effect and one to bring on Kedushas Shabbos. SiddurRavShabsai says three times. The YesodV'ShoreshHaAvodah says four time, once for each letter of Hashem's name. The Ben IshChai says five. The KafHaChaim says seven. The ChasamSofer would do ten. Other minhagim are thirteen or fourteen. (excerpted from Minhag Yisroel Torah)