When we were flying into Pisa airport (to get to Florence) we intended to take the train from Pisa to Florence.
However due to times being more convenient we took the Terravision bus just outside the arrivals terminal.
Absolutely no complaints and for €6 one way we got dropped off in Florence at Stazione Centrale di S. Maria Novella in just over an hour.
www.terravision.eu/florence_pisa.html
Just outside arrivals hall on right as you leave airport. There is a ticket office in airport.