Tuscany has two international airports, the Galileo Galilei International Airport in Pisa and Amerigo Vespucci Airport, also known as Peretola, in Florence. Located only 80 km apart, the Pisa airport is the larger of the two airports.
Both airports handle flights to major European cities. Pisa handles the bulk of European scheduled flights so it might be easier to find flights into Pisa if you're flying from Europe. If you're flying from further abroad, most airlines connect to major hub city in Europe and, from there, you can choose to fly to Pisa or to Florence. I recommend flying into Florence if you're planning to be here as your base, it will just be more convenient at the end of a long flight to get here and not take more trains or buses.
Direct flights from North America to Italy are generally more expensive than stopover routes somewhere else in Europe. More affordable fares can be had if one flies non-stop to a major European city such as London or Paris and then takes a Ryan Air (low-fare European airline) flight direct to Pisa. You'll have to change airports in London and Paris, though, as Ryan Air generally uses secondary airports. This might actually make it more convenient at that point to fly into Florence rather than Pisa. Depends on your plans and base you'll be using during your travels in Tuscany.
From the Pisa airport
By car: The Pisa airport has direct access to both the Firenze-Pisa-Livorno dual carriageway (Pisa Centro - Aeroporto exit), to the Genova-Rosignano A12 motorway (Pisa Centro exit), to the Firenze-Pisa A11 (through the Pisa Nord linking stretch with the A12) and to road SS1 "Aurelia". The terminal is also directly connected to Pisa Central Station by direct train service with many trains to the Pisa central station (there is currently work on the line so a bus guarantees service to the main train station) and with eight trains a day from the Pisa airport to the main Florence train station. The railway terminal is located just outside the departures hall. You can also reach the center of Pisa with bus or taxi service.
All major car rental companies are present at the airport, if you're looking to hire a car right away and drive to your destination in Tuscany. You can search for car rental offers here.
By train: If you land in Pisa and need to get to Florence, you can then easily catch the new PisaMover shuttle from the airport to Pisa Centrale and, from there, take a train to Florence.
By bus: There are also a few bus companies offering service to Florence right at the airport. For both, you can buy tickets when you arrive. Either will have you in Florence in about an hour.
From the Florence airport
The Florence airport also has direct access to the Firenze-Pisa A11 motorway as well as to the A1 "Autostrada del Sole". The airport is located on the north western edge of Florence; taxis and a bus shuttle connect the airport to Florence's historical center. You can read more about the Florence airport and connections to downtown in this article.
The Bologna, Milan and Rome airports are also larger airports you can fly into. You can rent car or take the train to Florence. Train or bus shuttles from all of these airports to to the the main rail line in each city makes it easy to reach Florence.