Where do I find all of the Daedric quests and artifacts in Skyrim?

Question

The only quest I completed was "Mind Of Madness" with Sheogorath, which was hilarious, and I would like to know where to find the rest of the Daedric quests.

Answer 1

All the Daedric artefacts are rewards for Deadric quests, here's a list of all of the quests:

• "Azura: The Black Star"
  • Start location: Azura's Shrine
• "Boethiah: Boethiah's Calling"
  • Start location: Read "Boethiah's Proving" (Known locations: Abandoned House in Markarth, on or under a bookshelf. The College of Winterhold, can be bought from Urag gro-Shub. )
• "Clavicus Vile: A Daedra's Best Friend"
  • Start location: Falkreath
• "Hermaeus Mora: Discerning the Transmundane"
  • Start location: Septimus Signus' Outpost
• "Hircine: Ill Met By Moonlight"
  • Start location: The jail in Falkreath's Guard Barracks
• "Malacath: The Cursed Tribe"
  • Start location: Largashbur
• "Mehrunes Dagon: Pieces of the Past"
  • Start location: Talk to Silus Vesuius (Dawnstar)
• "Mephala: The Whispering Door"
  • Start location: Talk to Hulda the bartender at The Bannered Mare in Whiterun
• "Meridia: The Break of Dawn"
  • Start location: Statue to Meridia
• "Molag Bal: The House of Horrors"
  • Start location: Markarth
• "Namira: The Taste of Death"
  • Start location: Discus rumours with Kleppr at the Silver-Blood Inn
• "Peryite: The Only Cure"
  • Start location: Approach Kesh at the Shrine to Peryite.
• "Sanguine: A Night to Remember"
  • Start location: Accept the drinking contest at any tavern.
• "Sheogorath: The Mind of Madness"
  • Start location: Solitude
• "Vaermina: Waking Nightmare"
  • Start location: Speaking to Erandur, in the Windpeak Inn in Dawnstar.

Source: http://elderscrolls.wikia.com/wiki/Daedric_Quests_%28Skyrim%29

Answer 2

Rare weapons, armour, and other items can be discovered from these quests for a list of rare enchantment weapons commonly mistaken for Daedric artifacts. Please refer to the "unique enchantments" page of the Elder Scrolls Wiki.