Perhaps the most time- and cost-effective way to reach Florence from Rome, Intercity Plus, Eurocity (EC) and Eurostar Italia (ES) trains ply the route from Rome's Stazione Termini to Florence's Stazione di Santa Maria Novella (often written Firenze SMN) in just under 90 minutes. Tickets can be bought and seats reserved at the ticket booth or its credit card-accepting ticket machines. You can also buy tickets and reserve seats through a travel agent or online at www.trenitalia.com or www.eurorailways.com. Reservations are mandatory on Eurostar and Intercity Plus trains and must be made at least one hour before the departure time. On these trains you can choose between first- and second-class seats (prima classe and seconda classe), the differences on the former including more leg room, more luggage space, the ability to recline and complimentary snacks. Also, don't forget to validate your tickets at the yellow stamping machines outside the station (failure to do so incurs a steep fine).
Intercity trains (IC) as well as locali and regionali, which are cheaper, typically older and slower (trip takes about three hours) than Intercity Plus and Eurostar expresses, make regular stops at major stations along the route. For the the adventurous with time on their hands, slower train options can often afford you a more authentic taste of Italy. Tickets can be bought at Rome's Stazione Termini. While no reservations are necessary on these trains, booking a seat is recommended, especially during rush hours, weekends, holidays and summer vacations when these trains can be packed with crowds.
Take the bus. A less common way to arrive in Florence from Rome, Greenline Tours (http://www.greenlinetours.com/servizi.php?lang=eng) connects travelers from Rome to Florence by bus for about $80, making it more expensive and slower. Also, Eurolines (www.eurolines.com) and SITA (www.sita-on-line.it in Italian) have buses running the same route, departing from Stazione Tiburtina.
Pick up a rental car through www.romewelcome.com/rent-car/rent-a-car-ing.htm, print out driving directions from www.maps.google.com and head northwest on the A1 (toll road). The trip covers about 180 miles of road and typically takes two hours and 50 minutes.
Although flying is not the most cost-effective way to reach Florence from Rome and hardly the most scenic, if you're in a hurry it could shave some time off your trip (though very little at best). Alitalia and Meridiana are Italy's largest domestic airlines serving Rome and Florence. Take off from either Leonardo da Vinci or Ciampino airport to reach Florence's small Amerigo Vespucci airport, named after America's namesake. Alternatively, fly to Pisa's Galileo Galilei airport and take a short train east, or fly to Bologna's Guglielmo Marconi airport and take a fast train south.