The quest "Amulets of Night Power" usually starts after completing the sidequest "Ancient Power". If you cannot get it to start, keep doing more side quests and main quests, then try again.

When you speak to Fura Bloodmouth in Castle Volkihar, or to one of the other vampires, and ask what you can do to help, they send you to Feran Sadri. Feran tells you he has located the last known resting place of a set of ancient Amulets of Night Power. They should be among our kind, not laying about unguarded for mortals to find.

This starts the Vampire Lord side quest:

Amulets of Night Power

Retrieve the Amulet of Bats from Darkwater Pass
Retrieve the Amulet of the Gargoyle from Broken Helm Hollow

Note: The locations of the Night Power Amulets are selected at random. For example, you could get sent to other locations, such as Broken Tower Redoubt, Serpent's Bluff Redoubt, Swindler's Den, or Bloodlet Throne.

Regardless of the locations you get, the rest of the quest is the same. Go to the dungeons specified in your quest log, fight the monsters there, and locate the amulet either in a chest, or as loot from one of the bosses. You can retrieve the amulets in any order.

You get:

Amulet of Bats
While wearing this amulet, Bats will drain life from any nearby enemies.

Amulet of the Gargoyle
While wearing this amulet, your Summon Gargoyle spell summons an additional Gargoyle for 30 seconds.

Both these amulets are very useful as a Vampire Lord. Make sure to put one of them on before transforming into a Vampire Lord, though if you are not planning on being in Vampire Lord form much, then the amulets aren't as useful.

Return to Feran. He gives you three blood potions as your reward, plus you get to keep the two amulets.

This completes the quest, Amulets of Night Power.