In only 30', an hour or an 1h and a half you can get to the Florence main Station from the three nearby airports.
If you arrive at the Florence Airport, it'll take you only 30' with “Vola in Bus” to get to the city center. The bus leaves every 30' from 5am until midnight everyday and you can take it on the right side of the main entrance of the airport, just across the line of the parked taxis. The cost is 6€ one way or 10€ return ticket and you can get it on board.
From Pisa you can take Autostradale bus or Pisa Mover + local train. You need 60' – 70' to arrive to Florence.
Bologna is good connected as well: you can find Appennino shuttles just in front of the Airport building. On the way to Florence, the bus stops only once and in 1h and 30' you're at the Florence main station. The bus leaves every 1h in the peek hours and every 2h in less frequented daytime. It costs 20€ for adults, 8€ for kids under 10 years of age and it's for free for kids under 4 years.
Florence stop is commonly called "track 16" or the side of the fortress that reaches down from the ramp of Romito.