Many of the people who work in Florence live outside the Historic Center, so public transportation is a major means of getting around. Some people have cars, and the Smart Car is very popular here. Florence has a very good bus system that runs the perimeter and inside the city, as well as a smaller line that goes inside the Historic Center. There is also a great train system that runs throughout Italy and all of Europe. Many people commute from outlying areas into Florence.
In a lot of areas in the Historic Center, cars are prohibited, and it is strictly pedestrian. That does not mean that you will not see the occasional "errant" vehicle, who is usually promptly chased by El Carabinieri. Police officers also patrol Florence via seque, horse, and on foot.
One of the most popular types of transportation is the scooter. The bicycle is also a hit. You can see these everywhere! They are parked in groves along the sides of the streets. High gas prices, narrow streets, lack of parking make these vehicles the vehicle of choice among Florentines!
For me, I have used the buses, taxis, trains. I had a scooter experience in Rome, but none yet here in Florence! Walking is my preferred method. I walk between 4-8 miles per day, not counting my 50 steps which I go up and down around 3 times per day! The odd thing is, I like it!