After completing the quest "The Legacy of Cain", talk to Deckard Cain who is now standing in the town center, near Leah. He tells you that the Skeleton King was once their beloved lord, Leoric, and was driven mad by Diablo's evil. Leoric lost both of his sons, and his very soul, before he was finally defeated. Now it seems he's risen to plague this land once again. The key to defeating Leoric lies in his old crown.
Deckard suggests you seek out the blacksmith, Haedrig, who knows of the crown's whereabouts. This starts the next quest:
A Shattered Crown
Talk to the Blacksmith Haedrig Eamon in northwest New Tristram
The spirits have revealed the truth to me. The Skeleton King, raised by the power of the Fallen Star, is responsible for the resurrection of the dead in New Tristram. If I destroy him, the attacks upon the town will cease. Cain has directed me to the village blacksmith, a man named Haedrig, who knows where Leoric's crown can be found. It is something I will need if I am to defeat the Skeleton King.
Before going to talk to Haedrig, you can ask Deckard some questions. If you ask him about himself, he tells you that he is the last of Horadrim. He couldn't always claim this. In fact, if he had turned to the Horadric Teachings sooner, Diablo could have been stopped before his reign of terror began. When the first signs appeared, Deckard did nothing. He shrugged the old tales off like they were so much fantasy, and Tristram and the world has paid dearly for his arrogance. He has tried to make up for his failings. Leah and him have spent her lifetime scouring the world, collecting pieces of the Prophecy of the End Days. If he can decipher it, you will have the key to defeating the Lords of Hell.
If you ask about the Prophecy of the End Days, you are told it is contained within the Horadric tomes Deckard inherited from his ancestor Jered Cain. It is a warning to those who could interpret it regarding Hell's ultimate invasion of our world, written by many different people throughout history in many different lands. All known versions of the Prophecy are incomplete. Deckard has spent a good part of the past twenty years trying to complete it. He is certain it holds the answers to defeating the Lords of Hell.
You can also ask Deckard about his relationship with Leah, and about Mad King Leoric. Regarding Leoric, Deckard tells you that Leoric resisted Diablo's attempts to possess him, but the effort left him weak and confused. When Leoric's son, Albrecht, was kidnapped to be a vessel for Diablo, it destroyed any sanity Leoric had left. After Leoric was the Skeleton King, he commanded an army of the dead deep within the cathedral, finally serving the Lord of Terror he had resisted while alive. Many adventurers tried and failed to slay the Skeleton King. It was left to Leoric's eldest son, Aidan, to finally kill the monster his father had become.
Talk to Leah as well. If you ask her about her relationship with Deckard, she tells you she has spent most of her life traveling from place to place with her uncle while he did his crazy research. Her uncle is convinced that the forces of Hell will invade our world and bring about the end times. All these years, he's still searching for a way to stop this apocalypse. When you ask her about her mother, Adria, she tells you that Adria wasn't from Tristram originally. She came here during the troubles. She was in search of something, but Leah is not sure what. Adria reminds her of Uncle Deckard, obsessed with the war between angels and demons.
Tashun the miner is nearby, you should sell him your extra items to unload your inventory and get some gold. Or you could sell to Arghus the Collector as well. When you are ready, it is time to find the Blacksmith. To get to Haedrig, head SW from the center of town, then head NW, towards the exclamation mark on the map.