The quest, Rising at Dawn, is an optional Side Quest relating to curing Vampirism.

Rising at Dawn Walkthrough

Make your way to any bar, such as Dead Man's Drink. Talk to the bartender and ask about any rumors he/she heard about.

The bartender will eventually tell you that Falion in Morthal studies vampires. Morthal is located near the north end of the map, southwest of Ustengrav. Falion is commonly located outside of town, and at night time you'll find him to the northwest. Talk 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 for roughly 150 gold.

Video Walkthrough

Filling the Black Soul Gem

Once you have the black Soul Gem in hand you'll need to fill it with a soul. You can use a Soul Trap spell on a human target and kill said target in order to capture its soul. Alternatively, you can use a weapon enchanted with binding to kill a target. If you don't want to kill any important characters, you can always wander the open world and wait for a bandit encounter.

Talk to Falion again once you have a filled soul gem and he will ask you to meet him at his mound at dawn. However, if you are blood-starved he won't help you. If you are blood-starved, you will need to feed on a human at night. See: Vampirism.

Simply talk to Falion at the mound at dawn (around 5:00 am works), say "Let's get this over with" and he will perform a ritual to cure you of your vampirism. It's over with.