You can get a bus from the centre of Oxford (I think it might have been called Magdalen Street), which is about a 10 min walk from the train station. I can't remember the bus number now, but I just asked one of the other bus drivers when I was there. From memory it took about 30 mins and stopped right outside the airport.
You could get a taxi, but I think it would cost around £20.
You could ask about transport on the OAA forum, you might get a better answer from one of the current students.