You’ll get either Azura’s Star (the fixed version) or the big Black Star respectively.

Hand over Azura’s Star to either big Aranea (from the quest’s beginning) or old Nelacar at the inn.

Steal his stuff along with that broken Azura’s Star. See that skeleton in his throne? Poor sod.

Soon you’ll hit a bunch of steps somewhere in the Deluge.

Keep on keeping on until you hit that barred door near the end.

Follow the Dungeon’s twisting corridors.

Strike out for Illinata’s keep (which be West of Riverwood).

After intimidating, bribing, or persuading Nelacar for info (Speech matters…Speech or money or muscle) He’ll let you in on the last known location of his mentor – who was playing around with Azura’s Star (Azura’s Daedric artefact).

He’ll point you to Old Nelacar (also in the inn).

Strike up a cheeky convo with Dagur at the Frozen Hearth inn.

Get yourself to the pretty standout Shrine of Azura – South of Winterhold.

Skyrim: Daedric Artifacts - Azura's Star & Black Star ('The Black Star' quest)

How to get daedric artifacts