Rising at Dawn

Walkthrough
If the Dragonborn becomes a vampire and wants to be cured, there is only one way to do so. Asking about rumours at various inns will eventually reveal that Falion is a mage in Morthal who specialises in studying draugr, vampires and the undead in general.

Speak to Falion
The Dragonborn can then proceed to Morthal and speak to the mage, who will immediately notice that the Dragonborn has contracted vampirism. He will then offer to cure the disease but ask for a filled Black Soul Gem for the ritual.

Bring a filled Black Soul Gem to Morthal
The soul gem can be obtained in any manner (Falion sells one for a leveled large amount of gold, Enthir also sells some) and if it is not already filled, then it must also be used to capture a soul from an NPC (lesser souls will not do). Once done, the gem must be brought back to Falion.

Meet Falion at dawn
The mage then arranges to meet the Dragonborn at the Black Marsh at dawn to perform the ritual.

Speak to Falion
At the Black Marsh, the Dragonborn must speak to Falion at dawn (between 5am and 6am).

Wait for Falion to complete the ritual
Falion then performs the ritual (which involves the screen fading to black) and cures the disease.

Erwachen im Morgengrauen