Put on your new wizard hat and then speak to the Image of Archmage Xylem just northeast of the Northern Rocketway Exchange.
- Approach Archmage Xylem while wearing your Wizard Hat
- Dingy Wizard Hat (Provided)
Every man's got to learn his own lessons I suppose.
Here, take my wizard hat. I have no doubt that he'll take you on as an apprentice if you look the role... you just might have to jump through some hoops first. Tiny flaming hoops, suspended over spikes, with spinning blades on the other side.
You should be able to find an image of Xylem on top of that hill to the northeast.