Florence's main train station, Firenze Santa Maria Novella, is located in the center of Florence. Most tourist attractions are within walking distance of the station.
Florence has two other, smaller railway stations, called Campo di Marte Station and Firenze Rifredi Station. If you wish to arrive in the center of Florence, you will want to skip them and arrive at Firenze Santa Maria Novella Station. Signs will usually say "Firenze SMN."
Firenze Santa Maria Novella Station is a terminus station. That means that the trains pull up to the station and stop, rather than pulling through the station.
Being an important station, high speed trains originate at Firenze SMN. Rome is about an 1 hour 40 minutes away and Milan is 3 hours away.
High Speed Day Trains serving Firenze SMN: Artesia, Cisalpino, Eurostar Italia (book fast trains direct)
Most of the important city buses (orange) stop across the road from the station on Via Valfonda. There is also a taxi stand is located outside the main entrance to the station, where you'll also find the Florence Sightseeing Bus.
There is a tourist information office to the left as you exit the station from your train. It's open from 8:30 AM to 9PM. You can book a hotel there for a fee.
The train information office is on your right across from track five (binario 5).
Near Track 16 is the left luggage, open 6am to midnight (subject to change).
You can buy tickets at the Salone Biglietti, or try using the automatic ticket machines. Expect long lines, especially during tourist season. I try to buy tickets for my outbound journey shortly after I arrive in Florence, since lines can be long. Ticket windows (sportelli) are open from 7:30 to 8 pm (subject to change).
Remember to stamp your ticket at the yellow machines before boarding your train. There is a large fine for not doing so. If you forget, try collaring a conductor on the train as soon as you can and explain your situation.