Free Public Transport
The Geneva Airport offers a ticket for free public transport into Geneva for arriving passengers. The machine above at the baggage claim exit will issue you a ticket. The ticket is good for 80 minutes in the Unireso system. This includes train or bus into Geneva, it will also work on the tram. Make sure to keep your plane ticket as proof of arrival.
The official airport has more information. Scroll down to "Travel free on public transport during your stay in Geneva". There is also the Geneva Transport Card offered to any visitor. It lets you travel for free in the Unireso network. Ask at your hotel, youth hostel or campsite.