From the main station (Zürich Hauptbahnhof)

• Tram No 10 (towards Zürich Oerlikon, Bahnhof or Zürich Flughafen, Fracht) until the Universität Irchel stop 
• Tram No 14 (towards Zürich, Seebach) until the Milchbuck stop
• Taxi (approx. CHF 25.00)

From the airport (Zürich Flughafen)

• Tram No 10, Glattalbahn, Flughafen Zürich until the Milchbuck or Universität Irchel stop
  (single ticket, 3 zones, zones 10;21: CHF 6.40) If you are travelling more than once, it may well be cheaper to buy a "Tageskarte" (24 hour ticket), CHF 12.80
• by train (SBB) to the main station (Zürich Hauptbahnhof), then Tram No 10 or No 14
• Taxi (approx. CHF 60.00)

Links

• Railway Switzerland: SBB
• Railway/Public transport region Zurich: ZVV
• Public transport city Zurich: VBZ (day pass/single ticket,
  multiple day passes/multiple tickets)

Tickets should be bought BEFORE boarding train or tram; there are machines at the airport, at all stations and tram stops.