You have to get bitten by a special type of Bloodfiend (players can infect you too) then a npc called Vorundil should be waiting by a wayshrine and give you the quest Scion of the Blood Matron, where you decide to become a vampire or to cure it. Check the page here for the abilitys to see if you think its worth it.
The bloodfiends should be at Bangkorai for Daggerfall Covenant, The Rift for Ebonheart Pact, and Reaper's March for Aldmeri Dominion and only at night.