Curing Vampirism
Activating any shrine of the Nine Divines will remove Sanguinare Vampiris but will not remove permanent vampirism.
Ask any bartender about any rumors going around, and he will tell you that Falion in Morthal studies vampires. Speak to him and he will tell you that, in order to perform the ritual, a black soul gem must be filled. To get the black soul gem, you need to speak to Falion again and he will offer to sell it to you (you can also obtain the black soul gem in other various, cheaper ways). To fill it, cast a Soul Trap spell on a human target and proceed to kill them, absorbing their soul. Now that your black soul gem is filled, return to Falion, who will tell you to meet him at dawn in the summoning circle. At the appointed place and time, you will be cured.
Notes:
Becoming a Werewolf also cures Vampirism. (This only works if you contract Lycanthropy as a quest reward; i.e from the Companions' questline.)
Potions of Cure Disease will cure Sanguinare Vampiris, the disease which progresses to vampirism, but will not cure vampirism itself.
Any bartender can tell you about Falion when you ask them about rumors enough times.
Falion will attack you if you are at the final stage of Vampirism (stage 4). Feed on someone to reduce the stage of your vampirism before visiting him.