In the following links you will find useful information about Florence: how to arrive in Florence, Florence airport and Pisa airport, public transportation and store luggage.
BY PLANE:
Florence has an airport (Vespucci, known as Peretola airport) where unfortunately not many international flights arrive to.
The most important airport which connects Florence is actually Galileo 'Galilei' located in Pisa which is comfortably connected to Florence via a direct train or bus (1 hour trip, costing between 5 to 9 euros). For bus information see this website (Terravision).
BY TRAIN:
Florence’s main train station is Santa Maria Novella, located in the historical centre of the city. Many trains also stop at Campo di Marte, another important station. These are all connected via trains or buses.
BY BUS:
Buses from the airport and other destinations generally arrive at bus stations next to the train station Santa Maria Novella. For bus information & to book tickets see the Terravision website.