You start in the middle of Psy Academy. You'll see a student in a Red Cape standing near you, talk to him. Just be nice to him and he'll tell you that Anya is looking for you and that she is likely to be found in her room. Go to the North East building and go into Anya's room.
Talk to Anya: she'll tell you that an old man is looking for you and that you can find him in the local bar. You can ask Piter, the Red Cape, where the bar is located and he'll direct you towards the North-West building. Inside, you'll find the old man, who turns out to be your Uncle, sitting in a corner- talk to him. You find out that your little brother, David, was kidnapped by the shadowlings and you need to rescue him.
Exit the bar, go north and find Guy, confide in him and by being honest (telling him there is a whole army of Shadowlings) get his support. Then go back to Anya's room and ask her for help: she'll be ready to help you too.
Proceed then to the South-East building and go into Administrative Offices. There, talk to the Desk Clerk and fill out the forms (it's worth noting that one has to pay a fee of 10 gold- if you've spent the money on gambling/buying books/lessons from tutors, you can ask Uncle Falstaff for a little cash and he'll give you, once only, 15 gold). Finally, go to the Guard watching over the West Gate and ask him permission to leave the Academy.You can also bribe a guard to let you leave(most probably in the west gate)with 50 gold but that is much more expensive and needs quite a bit of personality to work.