Flying into Rome, How to get the high speed train to Florence??

Take the Leonardo Express train from Rome Fumicino airport to Rome Termini station. I believe they run every 30 minutes. Fast trains from Rome to Florence run quite frequently. Check out the Italiarail or Trenitalia websites, where you can purchase tickets in advance at deep discounts. Unfortunately, since tickets go on sale 90 days beforehand, there may not be a lot of discounted fares left for the end of the month. But you might still find some deals. Just be advised that if you miss the train, you eat the cost of the tickets since they are non-refundable/exchangeable. I would book a train to Florence for about 3 hours after your scheduled arrival time in Rome to allow for flight delays, going through customs, etc. We did this exact trip in May 2014.

There are two trains that go directly from the airport to Florence every day. If you don't make either one of these you'll take the express train to the termini station in Rome and transfer to the high speed train there. There are many trains per day that leave for Florence from Termini. When you get to the train ticket office at the airport they will sell you tickets for the next train that you can reasonably catch. It might be the direct train but more than likely it will be the one leaving from termini. Don't buy train tickets for this trip before you get to Rome. If you buy discounted tickets and miss your train those tickets are worthless. Wait and buy at the station. The ticket seller will sell you the appropriate tickets. You'll pay the "base" price for these tickets. If you have other trips you plan to use the train for you can buy those in advance and save a lot of money.

Donna

Someone counted once - there are 53 trains a day between Rome and Florence. Take your pick.

Walk from the terminal 3 (your arrival terminal) to the airport station across the roadway using the pedestrian skyway (just see the signs). Buy the tickets to Florence at the ticket window there. The high speed trains to Florence that depart from the airport are only two, at 11:08 or 15:08. However there are two or three trains per hour departing from Rome main station (Roma Termini). Except for the two trains above, you will need to take the Leonardo Express train to Termini and change trains there.
I wouldn't bother buying ahead of time the discounted tickets. If there is a flight delay or at the passport control or at the baggage claim and you miss the train you book, you lose your money because discounted tickets aren't refundable. Just buy them at the station when you get there. It's about 60€ for a second (standard) class. Obviously if you can make the 11:08 train departing directly from the airport you save yourself having to change trains at the Termini station.

thanks for the response's!

Italian rail tickets go on sale 120 days in advance.