Azura's Star (Azura's Quest) Location - Morrowind
Location: Shrine of Azura & Island near Dagon Fel
Requirements: Do not enter Rayna Drolan's House
Video: How to get Azura's Star and Sheogorath's Signet Ring
Azura's Star is a reusable soul gem that's acquired by completing Azura's Quest, a side quest given to you by the Shrine of Azura. You can find the Shrine of Azura along the southeastern coastline of the main continent, the area is referred to as the Sheograd region of the game.
The easiest way to reach Azura's Shrine is to travel to Molag Marr via boat or Silt Strider then east from the town until you reach the shrine. Below the giant statue of Azura you'll find a door which leads to the Shrine of Azura. Inside there you'll find a smaller statue which you can interact with for a Journal entry.
What you need to do for this quest is to travel north of Dagon Fel to the island with Rayna Drolan's House on it - use my screenshot below if you're lost.
Warning: Do not enter Rayna Drolan's Shack on this island or you will fail the quest.
Once you make it to the island with Rayna Drolan's Shack you'll want to keep your eye out for a Golden Saint named Staada. Defeat her for a Journal entry and then loot the Sheogorath's Signet Ring from her corpse because we'll need that as proof of Sheogorath's meddling.
There are many other enemies on this island you can hunt down too if you want but only the Golden Saint is required. With Sheogorath's Ring in hand return to Azura's Shrine to complete the quest. You'll be rewarded with Azura's Star and you'll be able to keep the ring we got from the Golden Saint too.