Getting around in Florence

Walking is the best and often only way to get to many places in the center of Florence, unless you take a taxi (say, from the station to your hotel). Most likely, the only time you'll use a bus is to get to Fiesole, which is a small town on a hill above Florence, with lovely views. There is no Metro in Florence. I see this is the second city transit question you've asked. Do you have Rick Steves Italy? I highly recommend getting it, as he has detailed descriptions of transportation options for each place. For instance, he talks about electric minibuses in Florence and Rome that can go in the city centers, where standard size buses can't fit and so don't go, and he details which route numbers go where.

The easiest way is walk, the core of the historical center is only about one square mile wide. The cost of walking is free, if you can resist the temptation of entering those expensive boutiques.

Walk, definitely. The historic center is more or less a grid pattern of intersecting streets, hard to get lost and as Roberto said, the space is compact.

Ditto, esp. Harold and your guidebook situation (I'd recommend Rick Steves). The buses and trams can be really useful, depending on where you're going. Mostly, you'll be walking. The area you'll probably spend most of your time in is pretty compact.