You need to first, own the college…I assume you do if you know about authority, talking to Veronica and Madison will help (ask them their opinion), as well as reading the administrative manuals in the office and I believe one in the Library on the second floor (search)…but its not the main method.
In the office (same place you read the manuals and find Madison), you can ‘check your education level’ and ‘Raise Authority’…the important factor here is your education level.
When you try to raise authority if will tell you what your education level needs to be at, to raise your education level you need to teach classes in the empty classroom and NOT use your powers on the girls…I assume that option might be for a sexy scene down the road or just plain out to be funny, but it makes it so your education level doesn’t rise.
Note that doing any “Fey” classes seems pointless except for Pixie getting a new trait the first time, it doesn’t seem to raise your education level visibly.
So teach teach and teach some more during the week and keep going to the office between classes if your getting close to the needed education level (it doesn’t waste time) and try the raise authority option.