Zurich Airport is very well connected both to European and intercontinental flights. The university is around 20 minutes by tram from Zurich Airport (Tram 10 to Milchbuck). By train, you are in the heart of Zurich in 10 minutes. Trains and trams are very regular (around every 10-15 minutes all day) and a ticket from the airport costs 6.20 Sfr (valid for 1 hour to any destination in Zurich) or 12.40 for a 24 hour ticket. Your ticket is valid on train, tram and bus.
Switzerland's two other airports Basel (good for some low cost airlines) and Geneva are both very well connected by train to Zurich with travel times of around 1.5 and 3 hours respectively. Train travel is relatively expensive in Switzerland and if you are looking at these options, the Swiss Travel System might offer some savings over normal prices which you can find in the SBB timetable.
Zurich is also well connected by train to the rest of Europe, with CityNightLine offering overnight trains. Direct trains are available from many major cities including Milan, Vienna, Paris, Berlin and Brussels. The SBB timetable is a good place to start looking for connections to Zurich.
In Zurich, the easiest way to get around is by tram and bus. You can find a timetable here, but the general rule of thumb is that between 0530 and 0100 trams and buses run around every 10 minutes. A plan of the city network as PDF is here. Trams 7, 9, 10 and 14 as well as buses 69 and 72 go directly to the University (Irchel or Milchbuck).
You can find a plan showing the route from the tram stops to the Registration Desk here.