Geneva's Airport (Code: GVA) is serviced by 67 airlines from Aer Lingus to Varig. Service to/from Geneva is available from a number of countries, including the USA, Canada, India, Thailand, Brazil, and Australia.
The airport itself is located in the town of Cointrin, a very short distance from Geneva. Trains depart from the basement level Genève Aéroport station every 15 minutes for Genève Gare Cornavin (a.k.a. Genève Gare Central, or Geneva Central Station). Travel time is approximately 6 minutes. You also have the option of Buses 10, 23, and 28, departing for various destinations in Geneva. Fare is CHF 3.20 for train or bus (UPDATE: Geneva Airport is now providing a complimentary 80-minute Geneva Public Transport ticket to all arriving passengers who wish to take one. Check the website for details.). Obviously, it makes little sense to waste a railpass day if you're staying in Geneva.
If you plan to travel from the airport beyond Geneva, you can validate your railpass at the CFF (Swiss Rail) desk on the 2nd Level. Hourly Intercity or Eurocity trains depart from Genève Aéroport station for Bern and Brig. From Genève Gare Cornavin, you can make easy connections to many trains, including the high-speed Cisalpino to Milan and the TGV to Paris. Check the website for details on bus service to eastern France.
Geneva Airport is one of the world's smaller airports, yet has a wide selection of destinations including direct flights to the US, a number of Middle eastern cities and most big European cities.
The airport is well laid out, but has a tendency to have huge queues (more than 30 minutes!) at the terribly understaffed security checks. The remote gates (the 'B' gates) are quite a long walk underground from the main terminal and then a security check so don't wait until the last minute before heading for the gate! There seemed to be more desperate last-minute calls for passengers than I remember anywhere else. On a positive note, the security staff at Geneva Airport are genuinely friendly as well as being very professional - something that their counterparts in many other countries and airports should note.
The airport has a special French sector, as the airport lies on the French border and can be accessed directly from France without entering Switzerland. This means that flights to Geneva from French airports are domestic flights and also Geneva Airport can be used as a transit airport without needing a Swiss visa.
There is a major railway station at Geneva Airport with through services to Geneva (obviously) but also to Lausanne, Bern and Basel.
A taxi to/from downtown costs in the region of CHF35.
Most european airlines have connections here:
BA British Airlines
Unfortunately LOT dosnt flight there :(