An hour is *probably* just about enough, but I would leave a little longer.

I'm presuming your bags will checked through and you will already have your boarding card for the onward flight. In that case, you can expect to be in Zurich Central train station (Hauptbahnhof) within 45 mins of walking off the plane.

If you aim to be walking back into Hauptbahnhof two hours before your flight, you will have more than adequate time. The airport is called Zurich Flughafen - announcements on these trains are usually made in English too.

A return train ticket (CHF 12) will get you to and from the airport and let you use trams/ buses etc while you're downtown. You should get at least 2 hours downtown, and more like 2.5 if you push it.

Zurich Public Transport - http://www.zvv.ch/_tourist_e/default.asp