Zurich Airport is the largest and busiest airport in Switzerland, with flights throughout Europe and the rest of the world. It's located about 10km from the center of city. There are several options to make that journey.
Taxis are available but are by far the most expensive option. Fares can easily surpass CHF50. Your best bet is to take the bus or the train. Trains depart for Zurich every 10 to 15 minutes during the day, though less frequently very early or very late. A single ticket to the central Hauptbahnhof Station in Zurich costs around CHF7. A bus might be more convenient depending on your destination. Be sure to check out the route maps.