These quests are only available to vampires. After contracting vampirism, you will eventually be contacted by your tribe and directed to the questgiver. You'd think that would make you pals with all of the other vampires in the province, but that just doesn't pan out.
Like the Thieves and DB, you have an entry quest for your tribe. It's a standard dungeon crawl with a vampire as your object. After killing your target, report to the contact to be officially inducted into the tribe (you get a ring that marks you as a member). All Vampire quests should be launched by a summons at a random time though some players report being able to get quests from the original contact.
"<Tribe> summon you to <location>" (any rep): Deliver the letter as instructed.
"<Tribe> have a potential problem I fear. Come to me in <location>" (any rep): kill the rival vampire. Pretty much a standard dungeon crawl.
"Perhaps you remember a warrior you met once..." (any rep): seems one of your victims didn't stay dead and is now an embarrassment to the tribe. A standard dungeon crawl.
"Those doddering, unenlightened barbarians who call themselves the Mages Guild are involved in yet another rather pointless endeavor..." (any rep): the tribe wants you to retrieve the notes of a mage who is researching vampires in the Bay. If you are a member of the Mages Guild, they will also send you to retrieve the notes (which means you don't have to kill the old man), but you can turn them over to the tribe instead (probably taking a slight hit to your rep with the Guild).
"We have a small task for you to perform to prove your resolution to be one of us..." (any positive rep): retrieve the item from the Mages Guild.
"We are having difficulty with a local warlord who, despite our many, many polite verbal and written threats, continues to wage a war against <tribe>..." (rep 10 or more): a standard dungeon crawl, but you are not supposed to kill your target -- just rough him up a little.
"<Tribe> have need of you. Come immediately..." (rep 10 or more): go to the dungeon and whoop up on the Daedra for the honor of your tribe. Standard dungeon crawl.
"<Tribe> need you. Come immediately..." (rep 10 or more -- notice the difference in the wording of the summons): escort the vampire to his destination without getting killed by the vampire hunters along the way.
"<Tribe> need you. Come immediately..." (rep 20 or more -- you'll just have to talk to the questgiver to find out which one this is): standard dungeon crawl with a wereboar as your object. He'll have a tusk as part of his treasure which is your proof you accomplished the mission.