The train system in Geneva is one of the most convenient ones in Europe. Local trains run every half hour in the daytime, and every hour after 8 p.m.
The central train station, Gare Cornavin, links to the airport and also to almost every accessible area of the city. You should, however, beware of pickpockets in and around the station.
Check the company's website (www.sbb.ch/en/index.htm) for other details, inlcuding timetables and destinations.