Another way of getting around is by using the public buses from ATAF. A day ticket costs €5 and a 3 day ticket costs €12. A four-ride ticket costs €4.50.
You can buy tickets at tabacchi (shops selling tobacco, which are marked with official looking "T"s out front." kiosks/newsagents/bars where the symbol "Biglietti ATAF" is shown, as well as at the ATAF ticketing office at the bus station outside Santa Maria Novella train station. Several ticket options are available. One very convenient is the 4-rides ticket and the "Carta Agile". The former needs to be stamped when entering the bus (from the front and rear doors of buses - the central door is supposed to be exit only; though now it is more accepted to enter from the central door).
The latter has an embedded electronic chip and needs to be held close ("swiped") to the upper part of the ticket machine inside the bus: the "beep" of the machine will inform you that a ticket has been paid and the display will show you how many more tickets ("swipes") you have left. Within 1hr of stamping/swiping you can hop-off & hop-on on any bus of the urban ATAF network. Unfortunately and completely against Italian law, it is not uncommon to see bus drivers talking merrily on their mobile phone while driving. Don't expect riders to complain about it and don't panic - they will still drive with the same non-comfortable style as when they are "only driving". Hold tight to hand rails as Florence traffic is very unpredictable and frequent sudden braking is necessary. Bus rides are not by all means "smooth". Buses are "safe" but pick pocketing is quite common. Please keep a close eye to your belongings and avoid showing off cash/jewelry/etc. especially in very crowded buses (especially for lines 17/23/14/22 - generally speaking any crowded bus can give a chance to pick pocket).
Bus stops have clear, schematic labelling of the routes and are all named according to the street name or major landmark nearby. They do not always give an indication of bus times, however, so it is sometimes difficult to figure out how long it may take till the next bus arrives. Tickets must be bought in advance from Tobacconists or newspaper sellers, and are usually valid for one hour over the whole network, so that you can just hop on and off at will. They cost €1.20 for 70 minutes, and multiple day tickets are also available. Tickets are also available on the bus, sold by the driver, at an increased price of €2 (therefore, no more excuses in case of ticket control).