Use bus (see here) or taxi (appr. 20 euros). Taxis or taxi-vans from the airport to the center of the city/Aristotle University of Thessaloniki: mail: fntaxivan(at)gmail(dot)com – mobile: 6909000530 – 6974443430
Get informations about the public bus routes and timetables at the official site of the public transportation of Thessaloniki: here and here.
The bus tickets cost 0.80 euro and 0.90 euro when bought on the bus. If you want to change buses you need a ticket for two buses (one direction always). It costs 0.90 euro and on the bus 1.00 euro. Be careful the ticket machine on the buses doesn’t give change.