There is a train station inside the airport building. Take the train to "Zurich HB" (main station).
Tickets: You can get tickets at the corner or from the automat.
1st: Get a "zone 10" ticket. It covers all train/bus/ship connections in Zurich city. A return ticket is twice the price but valid for 24hours - CHF 7.60.
2nd: You need an additional (single) ticket "added zone" to cover the trip from Zurich airport to the city - CHF 4.20 app.
From main station:
Take the (green) tram Nr.3 until Klusplatz. Follow the direction for another 100m. On the left hand there is house no. 43. Top floor, top dor bell.