Getting around Geneva is fairly easy by foot, as long as you plan on staying around the old city, though you should expect to deal with some of the hills.  However, the Transports Publics Genevois will take you quickly and efficiently anywhere else you may want to visit.
Most trams leave from the stops right outside of Gare Cornavin, the main train station, and you can also catch them at Place de Bel-Air in the old town. 

Every hotel in town issues a free public transport pass for its customers. That way, tourists do not have to pay to use public transportation. Just ask the reception when checking in.

One great option is renting a bike for free to wander around Geneva. While it’s not the best idea in the old town, it is a great way to explore the rest of Geneva.  Geneve Roule is a program that offers free bike rentals for a day (usually until 7pm) in exchange for holding your ID plus a deposit of 50 Francs; all of it is returned to you once you return your bicycle.  The only downside of this program is that some of the bikes have ads on them, so you may actually want to rent a bike from the train station if you’re too stylish for that.  This program also runs in Zurich, Lausanne, Bern, Neuchatel, and Thun.   It is advisable to wear a helmet when you ride a bicycle, and to be at least somewhat familiar with the traffic rules.  Also be aware that Geneva has a great many one-way streets and some areas are restricted to pedestrians.  When you get your bike, ask for advice!