When you reach dungeon level 3, go back to town and talk with Odgen. He will talk about Archbishop Lazarus' betrayal, the kidnapping of Prince Albretch and the madness of King Leoric. The king sent all the warriors to die with him in the dungeons, and it was all premeditated by Lazarus. He will tell you to set free the suffering soul of Leoric, so the people of Tristram could have more hope. Go back to the dungeons and find the entrance to his domains at level 3.
There isn't much to say about this place, since the lead will take you to King Leoric's Cursed Squeleton. All the demons on this place are squeletons (archers and captains), and they will come in a huge horde, so be careful! A useful thing is to use Holy Bolts on them, since their bonus against undeads is great.
When you reach Leoric's Squeleton, don't try to kill his minions since he will keep resurrecting them. Go directly to Leoric and crumble him to death. Try not let him slash you, because that will make you stop attacking and will keep bringing you closer to him. And he slashes quickly, killing you in a matter of seconds.
If he hits you, drink some potions so you don't die and try to walk far from him. Then go back and continue attacking until he dies. After he's dead, he will drop his Undead Crown (useful at the beginning), or some magic item if you get unlucky.
After defeating Leoric, go to every corner of his room and click on each four crucified skeleton, making them fall. That will open a secret door filled with skeletons. Defeating them will increase your chances of getting some good loot.
If the quest is still on your quest page, simply back to town and talk with Odgen.