Florence has one of the biggest Airports in Italy. Flights from all over the world reach Florence everyday. You ideally should reach Florence and from there you have various options to choose from to reach Siena.
You could take a train to Siena. However, buses are more convenient as they leave in every 30 minutes and are faster than the trains.
Transportation in siena
Take a Bus or a Taxie to The Central Train Station of Florence. Right where the Taxi or Bus drops you is the Inter State Bus Depot too, so you have two options from here to reach Siena. You can also travel by private vehicles or hire cabs.