If the Dragonborn urges him for more information on the guild, he will direct them to Brynjolf in the Riften Marketplace, or if the time is night, the Bee and Barb.
He will also state that Vex can only be spoken to if one is a member of the Thieves Guild. After speaking to him, he will tell the Dragonborn what he knows of the gem, and requests they speak to Vex in order to find out what the gem is worth. Once at least one is discovered, the quest will be eligible to be started. Unusual Gems can be found all over Skyrim. Bring the Unusual Gem to Vex in the Thieves Guild.
I should bring it to someone knowledgeable in such goods for appraisal. I've found an unusual gem which seems to exhibit magical properties.
