Arriving by plane at FLR Amerigo Vespucci airport you can reach the city center by taxi - the ride is about 15 min (according to the traffic) and it will cost about 25 euro.
You can also take a bus VolaInBus ("Fly in Bus") to the central train station (5 euros) and then take a taxi from there to the hotel (less than 10 euro in every location of the city center). The bus goes from a small bus shelter which is to the right hand side as you walk out of the airport. Its beyond where the taxis are queuing. Not obvious at first but it is a quck and efficient service.
Arriving at PSA Pisa airport you can reach Florence by taxi - 80 km it will cost about 100 euro - or by train which is directly connected with the air terminal (sometimes requiring a change in Pisa Centrale station - about a one hour ride for about 6 euros). There is also now a VolaInBus service to the Florence SMN train station.
Arriving by train at Santa Maria Novella station you are right on the city center. Many hotels are located nearby the train station or are walking distance from there. If you take a taxi from there you can reach every area of the city center for less than 10 euro. To get a taxi you have to take the left exit of the train station and make the line. Or take a local bus. There's a map of bus routes in Florence here. Florence is linked to many locations via Italy's excellent railway services.
If you arrive in Florence just for the day and have a back pack or hand luggage (small suitcase), it can be left safely at the station, all day. The charge in 2009 was € 5 for first 6 hours and the 20 cents for every other hour. They take a copy of your Passport or Identification. The place is by Platform 16.
Arriving by car you have several options:
Arriving from NORTH or WEST take the motorway exit "Firenze Nord"
Arriving from SOUTH (ROME) take the motorway exit "Firenze Sud"
Arriving from SOUTH (SIENA) take the motorway exit "Firenze Certosa"
Bear in mind that the heart of town is off-limits to private vehicles (ZTL - Zona Traffica Limitata), but your hotel will register your car asking for the number plate upon your arrival. Ask for specific directions. Take special care not to pass over the Bus only restricted streets. In that case, the registration in the hotel can't cancel the penalty. Be careful with rental cars - if you are not going to your hotel or the rental car agency to return it, you may find a 70 euro fine on your credit card (from the police to the rental agency to you) later on. You then owe it.
If you are departing on a 6:30 am flight, don't plan on being there any earilier than 4:30 am when the airport opens and the staff are ready at the counter. You can save a lot of time at the counter by using the kiosks to print out your boarding passes.