The Crown of the Skeleton King is a quest item found on the second level of the dungeon below the Tristram Cathedral. It's dropped by the leader of a group of Dark Summoners, and can not be equipped. The crown should be picked up and taken down to the third level, to Leoric's throne. Drop the item on his bones and Leoric's spirit will be called back to his body, and he will rise up, full of malice.
Information on this page is based on how the quest was presented in the Blizzcon 2008 demo. Details will likely change in the final game.