Arriving from Rome airports
Rome has got two airports, Fiumicino (FCO) and Ciampino (CIA). Fiumicino, whose official name is Leonardo da Vinci airport, is 310 km distant (using A1 motorway) while Ciampino is 290 Km far (2 hours and 40 by car) from San Casciano in Val di Pesa. Fiumicino is the busiest Italian airport, is connected to all the world (USA, Brasil, Japan etc..). Ciampino is served by many low cost airlines like Ryanair, easyJet that connects Rome to many European cities.
Fiumicino flights departures and arrivals
The complete list of Fiumicino airport connections is on the official airport site and on this Wikipedia page.
From Fiumicino without a car
There is a direct connection by train from Fiumicino airport to Roma Termini railway station, the trip takes 30 minutes and costs 11 euros (price as of March 2010). Alternatively it is possible to take Sabina-Fiumicino (FR1) line to Roma Tiburtina; usually every 15 minutes, and every 30 minutes on holidays. For more information visit fr1 line page on Trenitalia website. From Roma Tiburtina get a regional train (0,90 euro, 11-17 minutes) to Roma Termini.
Once in Roma Termini, you can get a train to Firenze Santa Maria Novella. The fastest (and more expensive) are called Eurostar AV, will get you to Florence in 1 hour and 35 minutes for 44 euro. Once arrived in Florence, get out of train station from the right, walk for 80 metres to Autostazione SITA in Via Santa Caterina da Siena, buy a ticket and get on a coach to San Casciano (about 35 minutes trip).
Summarizing the trip after you have landed in Rome Fiumicino: 30 minutes to reach Roma Termini, 1 hour and a half to reach Florence, 30 minutes to reach San Casciano in Val di Pesa.