You can find out the latest connections between Zürich Airport, University and Martahaus/ Main Station by going to http://www.zvv.ch/fahrplan.htm. Your from or to location (in german: Von or Nach) is Airport, Hauptbahnhof (Main Station) or Irchel (University)
Tram stops at the University Irchel are Irchel and Milchbuck.
You need 15 - 30 minutes from the Airport to the University or Martahaus/ Main Station.
The Martahaus is located close to the Main Station (15 minute walk). Please have a look at the map.
Pay attention that the Zürich summer school takes place at the University Irchel and not at the University Zentrum/Rämistrasse.
Some helpful maps: University of Zürich, University of Zürich, more detailed, Irchel buildings