Hern the vampire at Half-moon Mill.

Becoming a Vampire Whenever a vampire casts Vampiric Drain on you, there is a chance for you to be infected with Sanguinare Vampiris. Initially, this is a normal disease that reduces your total health by 25 points. It is subject to the rules which govern any other disease, and can be cured in the same fashion. However, not curing the disease within three days will cause it to progress to full vampirism. At that point, the effects can no longer be reversed with a normal cure. Sanguinare Vampiris gives messages to the player each day at certain times, indicating their condition. At sunrise, a message will appear saying "You feel strangely weakened by the sunrise". At sunset, the message is "You feel a strange thirst come over you". After the third day, Sanguinare Vampiris will disappear from your active effects and you will awaken as a stage one vampire. There are many ways to contract the disease, all of them involve encountering hostile vampires and letting them attack you. However, rather than let them hit you in melee, you should keep your distance and only allow them to cast their draining spell as this is the only attack that can impart the disease. To speed up contraction, repeatedly lose and gain sight of the target vampire so the spell is cast multiple times. The check for giving you the disease is passed only when the draining spell hits you, not over sustained action. One can travel to the Blue Palace, located in Solitude, and talk with the court wizard Sybille Stentor. She will tell you that there is a vampire problem in Pinemoon Cave, and ask you to deal with it. Simply follow the Misc. quest marker to the cave, arm yourself with healing spells/potions, and let the vampires attack you until you catch the disease.

http://www.uesp.net/wiki/Skyrim:Vampirism#Becoming_a_Vampire