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You'll receive this quest from Onmund at the College of Winterhold when you ask him what's wrong.
Onmund will tell you that he traded an amulet to Enthir, but that it's a family heirloom and he'd like to get it back. Since Enthir will no longer speak to him, Onmund will ask you to act as an intermediary and figure out a way to convince Enthir to return it.
When you talk to Enthir, you might be able to persuade him to give the amulet back, but chances are you'll have to complete a task for him. For that case, Enthir will tell you that he traded a staff to somebody, but that he's now worried about how it might be used, and so he'll offer to give you the amulet if you can get the staff back for him.
The staff will be in a random location, including places like Movarth's Lair and Yngvild. You'll typically find the staff being guarded by a spellcasting boss. After tracking down the staff and returning it to Enthir, he'll give you Onmund's Amulet as promised. Then when you give the amulet to Onmund, he'll become available as a follower.