Florence is a very walk able city but you will need to use Florence's public transportation system to travel to the outskirts of the city limit and use Trenitalia and SITA to travel to other cities throughout Tuscany and surrounding cities.

To get from Amerigo Vespucci - Peretola (FLR) airport to Florence and vice-versa use the shuttle bus run by Busitalia - Sita Nord marked with the name Volainbus.

Stazione Santa Maria Novella (SMN) Train Station connects you to major cities throughout Italy serviced by Trenitalia's high speed and regional trains.

Use SITA bus system located across the street from the SMN train station to escape Florence for the day or a few days to popular cities within Tuscany like Siena, San Gimignano, and Arrezzo.

I have never used Florence's bus system as I love exploring the city by foot but there are a few cases I'm sure where a bus would be best served by Florence's ATAF bus system.