Destroy the Ash Guardian
Notice! This mission will be available only after you complete Path of Knowledge!
After completing any of the side mission in Tel Mithryn and return after some time, you should be approached by Talvas. The terrified apprentice will ask you for help - in the result of a failed experiment, he summoned a powerful Ash Guardian who now wrecks havoc in the region. You need to kill the monster before master Neloth notices what happened (Talvas will draw away his attention).
The monster is surprisingly weak - he can use some medium range spells, but has very little health, so you will easily defeat him. After the fight, return to the tower in Tel Mithryn and tell the worried apprentice that everything's over.
Talk to Talvas
Meet with him at the top of Tel Mithryn to end the mission. In return you will receive a magic staff - the Minor Staff of Turning - and additionally will be able to trade with Talvas, take him to your team or even train Conjuration.
If his behavior has made a exceptionally bad impression on you, you can always tell Neloth - however that way you won't be able to ask Talvas to join your team.