Bring the Unusual Gem to an appraiser

Walkthrough
There are a number of Unusual Gems scattered around Skyrim. As soon as the Dragonborn finds one, this objective is added to the journal and a map marker for Riften is added to the map. Once in Riften, simply ask around about the gem.

Eventually, the Dragonborn will be directed to speak with Vex, a member of the Thieves' Guild who reveals that the unusual gem is in fact a Stone of Barenziah, and that there are 24 of them in total.

Bringe den ungewöhnlichen Edelstein zu einem Schätzer