The main train station in Pisa is called Pisa Centrale - from there you can catch the shuttle to the airport, it takes about 8 min, and from there rent a car from any of the major car rental agencies - Hertz, Avis, Sixt Rent a car, Maggiore, Europcar and Budget. All of them are at the airport since it is so close, they don't have offices near the train station.