To come to Florence you can fly directly to Florence Airport or to a near by Airport as Rome, Bologna and Pisa.
If you fly directly to Florence airport, you can get to downtown Florence either with a taxi or with the special “Vola in Bus” bus shuttle that you can take from the airport to the central Santa Maria Novella train station (SMN). It takes about 20 minutes, sometimes a little more if there is heavy traffic. The service runs daily, including Sundays and holidays.
If you fly to Rome, you have two airports: Fiumicino Airport and Ciampino Airport. If you fly to Fiumicino you can take a train from the airport directly to Florence station. You can buy your ticket at Trenitalia or directly at the airport. If you fly to Ciampino Airport, you have to take a bus shuttle to Pisa central station and from there take a train to Firenze Airport.
If you fly to Pisa you can take a bus or the people mover to Pisa central station and from there take a train to Florence central station. You can buy your ticket in advance at .Italo and Trenitalia or you can also buy your ticket directly at the train station.
If you fly to Bologna you have to take a bus from the airport to Bologna central station that costs 6€, you can buy the bus ticket in the machines at the airport. If you have the opportunity to share a taxi it is better than wrestling with lots of luggage on the crowded bus, the taxi would cost around 20 euros to the central station. From the central station take a train to Florence train station Santa Maria Novella. You can buy you ticket in advance at .Italo and Trenitalia or you can also buy your ticket directly at the train station.
If you fly to any other airport you just have do the same as in the airports above, going to the central station of the city and take a train to Florence central station.
Be aware that Italy is a very touristic country and tourists attract scammers and thieves, and airports and train stations are a common target for them. Please beware of your belongings at all times.