Florence Santa Maria Novella (Firenze SMN is how you will see it on train schedules) is Florence's main train station. The station handles more than 400 trains and a 160,000 people a day! Many bus stations (SITA, CAP for Prato and west of Florence) are nearby and there are also ATAF (local Florence line - usually orange) buses to be caught on either side of the station. A lot of car rental agents are just a few blocks away, many on Via Ognissanti. There is a car park underneath the station as well, and there is a taxi stand outside the station with an endless supply of white cabs.
You can find a list of information and usual services available (pharmacy, food, post, luggage, etc.) at the station here, and you can purchase tickets (or at least plan your itinerary) on the main Ferrovie website (there are reports that you can not buy tickets on this site without an Italian credit card).
From Firenze SMN you are about an hour and 40 minutes to Rome, 2 hours and change to Milan, less than 3 hours to Venice (on most trains), and 3 to 5 hours to Naples.