Geneva Airport is on the west side of Switzerland, near the border of France.
If possible, it's better to fly into Zürich, since it is about 1 hour closer to most popular destinations in Switzerland. But if you must fly into Geneva, the Genève-Aéroport train station is directly at the airport, giving you convenient access to many Swiss cities and mountain destinations.
Train connections
Here are some travel times from Geneva airport (aka Genève-Aéroport) to nearby cities.
Geneva city (aka Genève): 7 mins / direct trains every few mins
Lausanne: 52 mins / direct train every 10-20 mins
Montreux: 1h14 / direct trains every 15.20 mins
Travel time to other popular destinations
Bern: 2 hours / direct trains about every 20-30 mins
Interlaken Ost: about 3 hours / 1 transfer in Bern
Zermatt: 4h / 1 transfer in Visp
Lucerne (aka Luzern): 3h16 / direct trail hourly, otherwise 2 transfers
Zürich city (Zürich HB): 3 hours / direct trail hourly, otherwise 1 transfer
Timetable
You can check the timetables on the SBB Mobile app and SBB.ch. Before your flight, it's helpful to check the possible connections, so you know what to look for.
The signs above the track show upcoming departures with train number, destination, and departure time.
Tickets
Train journeys are free with Swiss Travel Pass, Eurail, and Interrail passes.
If you need a ticket, you can buy it on the SBB Mobile app, ticket machines next to the train track, or ticket counter/info desk near the tracks. Discounted 50% with Swiss Half Fare Card and for children age 6-15. Children under 6 ride free with parent.
Once you have a valid ticket or travel pass, you can just get on the train. You do not have to scan your ticket or show it to someone. Random checks are done on the train. If you have the Swiss Half Fare Card, you will need to show it along with your discounted ticket.
You will get a fine if you cannot show your valid ticket/travel pass.