Diablo 3 Walkthrough Part 18: Desolate Chamber

After you kill the Skeleton King, your task is to enter the Desolate Chamber. First though, pick up any loot the boss had dropped. Most likely he had dropped a rare (yellow) item, sometimes unidentified. The game will tell you:

Unidentified Items
You have picked up an unidentified item.
Right click on the item to reveal its magical properties.

Follow the instructions, and right click on the item to identify it. Equipping it gives you the following achievement:

Rarely There
Equip a rare (yellow) item.

The above achievement comes with a reward, Banner Pattern - Right Stripe.

You should also have received an achievement for killing the Skeleton King:

The Mad King's End
Kill the Skeleton King on Normal Difficulty.

This campaign achievement also comes with a reward:  Banner Shape (Holy)

The entrance to the Desolate Chamber is where the Skeleton's King throne used to be. Enter it, and your next objective in the "Reign of the Black King" quest is to talk to the stranger in the Desolate Chamber. You should find him near the crater. Go around, and down the stairs. Speak to the person with the exclamation mark on his head, standing in the center of the crater. He tells you he remembers falling. He tells you he is not your enemy. He has come with a warning. The darkness is coming. You tell him that you will take him to Cain. Your next step in the quest is to return to New Tristram. Use the town portal skill, or head towards the waypoint on the map.

There will be a cutscene. You have learned that the fallen star is not a comet, but a man who does not remember who he is. You will bring him to Deckard Cain who perhaps has the answers. Your last task in the quest, once you reach New Tristram, is to speak to Deckard Cain. Talk to Deckard Cain and introduce him to the man who you claim is the Fallen Star. Deckard says that no man could survive such a thing, and asks the stranger who and what he is. The Stranger says he thinks he is a warrior. He came bearing grave news, but he cannot remember. Deckard thinks that the stranger's message might be all that can save us from impending doom.

This completes the quest, Reign of the Black King.