As you enter the Cemetery of the Forsaken, you received your next objective:

A Shattered Crown
Search for the Chancellor's Altar beneath the Cemetery of the Forsaken.

On your map you should see big orange gates, which are entries into the tombs below the Cemetery. You will have to go into each of them and search to see if the Chancellor Altar is there. Even if you find the Altar, you should still explore all remaining Crypts though. Many of them have treasure hidden in them. Others could have side quests and events. When exploring a crypt, be on the lookout for Stone Vaults, which you can interact with and receive all sort of loot, including rare items and gold.  Some of the crypts will have Imps in them, who are small creatures of the Demon race.

Be careful while exploring the narrow corridor of the crypts, as you will be swamped by those imps. As you kill them, be sure to use the red health globes as they spawn. You use a health globe by just walking near it (there are also some abilities that increase the range from which a health globe is effective). Other enemies in these Crypts will include Skeletons, Hungry Torsos, Hungry Corpses (Teleporter), and more. There could also be some Elites in these tombs.

On the surface, you might find red healing wells. Use them to replenish your health in between searching the tombs.

Some tombs can have Shrines, such as Enlightened Shrines, which give you blessings of some sort, including +25% Experience. But watch out for Tomb Guardians, that are protect the tombs and can be quite powerful.

There are events to be found in the tombs. For example, you might run into Lady Dunhyld, who tells you that Grave Robbers have defiled her tomb, and her husband writhes in torment because she does not rest at his side. She asks you to return her bones so that she and her husband may rest in peace. This unlocks the Event (kind of like a side quest) in which you need to help put the spirit of Lady Dunyhld to rest.

The Matriarch's Bones
Search the Funerary Urns for the bones of Lady Dunyhld (0/3)

Diablo 3 Lord Dunhyld

Search the dungeon for Funerary Urns, and when you find them interact with them. Prepare for combat after interacting with each Urn, including one against a boss, Lord Dunyhld himself (Phantom of Anguish). Lord Dunyhld appears each time you interact with one of the Urns, and you have to defeat him a total of three times.

After you have found all the bones, you have to place Lady Dunhyld's bones into the Dunhyld Sarcophagus. Locate the Sarcophagus (A yellow arrow and blinking circle on the minimap should help guide you to the location). Place the bones on Dunhyld's Sarcophagus to get a nice reward including experience and gold, as well as an achievement with the same name as the event:

The Matriarch's Bones
Complete the Matriarch's Bones event

Another small event that you may stumble upon is:

Jar of Souls
Look for a blue jar hovering about a pedestal. Interact with it, and be prepare to fight scores of restless souls. Try and stay alive for about 60 seconds to complete this event, and receive a gold and XP reward. Use a health potion if necessary.