All major attractions are within walking distance of each other and so you probably won't use public transport much!
Public buses are provided by ATAF. You can buy tickets at kiosks/newsagents/bars where the symbol "Biglietti ATAF" is shown, or at the bus station outside Santa Maria Novella train station. There are many type of tickets available including a day ticket €5, a 3 day ticket €12 and 4-rides ticket at €4.50.A single ticket is around €1.20. Single tickets are also sold by the driver, but at an increased price of €2.
Depending on the ticket you will either have to swipe it or have it stamped in the machine on the bus. Tickets are usually valid for about 70 minutes on the whole network, so that you can just hop on and off at will.
Florence does not have a metro (subway) system!
The main station is Firenze Santa Maria Novella, on the edge of the historic old town. From here you can take local and express trains to other parts of Italy and Eurostar trains connect Florence with Italy's main cities and other European countries.
Ticket prices are good value!
You do not hail a cab from the street in Florence, instead you either call for one or get one at a taxi stand, which can be found at the main train station and several popular squares and tourist spots. Taxis can be expensive in Florence! (Call 055 4242 for a taxi operated by socota, or see web site below)
Driving in Florence is not recommended as no one seems to obey any rules, plus the streets are narrow and car parking is almost impossible to find in central Florence. Use a car only for trips outside the centre of Florence !!!
(Taxi in English)
Official Trenitalia Train Web Site