Landing in Pisa can be very unpleasant for a traveller accustomed only to big and organised airports. Since Pisa is a small city, it has a little airport. It's functional, tidy, and clean, but really small. Anyway, I don’t think you’re interested in airport architecture, so I’ll give some essential advice on what you can find in this airport.
First of all, when you book a flight to Tuscany and want to land in Pisa, be sure to book for PSA, not Florence airport, because they’ve unified the bookings for flights. Notice that Florence and Pisa are not so close; it takes about an hour and a half by train to get from one to the other. So if you're going to Pisa and you land in Florence after hours and hours of travelling, you’ll probably be unpleased to have to travel another hour by train. I prefer to underline this fact because some friends of mine made similar mistakes.
Anyway, let’s start with some practical information. First of all--important for backpackers--the airport is closed during the night. It closes after the last flight (it depends on the season) and opens at about 5:30am. In the airport, there are many car rentals, an ATM, and some shops. Regarding the rentals, check the opening hours by phone--many times, on my arrival, they were closed (I had no booking).
Transportation:
Trains
There’s a train station just outside the airport, called "Pisa Aeroporto", that's useful to get directly to the main station, "Pisa Centrale", or to Florence "Firenze S.M.N". I don’t suggest you take the train to go to the central station, as it's better to take the bus.
Terravision
This is a low-cost coach service between Pisa and Florence, in partnership with low-cost airline, "Ryanair". So check their website for the schedule--it varies according to Ryanair's flight changes: http://www.terravision.it/florence_pisa.html.
Cabs
I’ve never used cabs to get to the city centre, since it’s not so far away. Usually cabs in Pisa are not expensive.
Bus
There’s a bus stop just outside the airport, and you only need to buy a ticket at the newsstand. But be careful--if your flight is scheduled to arrive after 8pm in Italy, it can be a problem to find a bus. It would be better take a taxi in this case.
In the last 5 years, Pisa airport has become an important hub for low-cost airlines, so if you plan to visit Europe in a cheap way, think about Pisa.
I’ve personally been to London, then again to London/Aarhus and to Brussels with Ryanair. If you find a good offer, you can travel from Pisa to Bruxelles with 30 euros round-trip, including taxes. Main low-cost airlines are Ryanair, Hapag Lloyd express (Germany), and Transavia (Amsterdam).
Check the official websites frequently to find offers and more information.
This is Pisa airport's homepage: http://www.pisa-airport.com/.