Rome airport to Florence

You need to remember where you put your wallet.

The process is simple. You can buy at the ticket window or at an automatic kiosk (prompts are also in English).
I would start with printing the schedule so you know all your options. Then you take the one that is most convenient depending on the time of arrival at the airport station (across the Terminal 3).
Go to www.trenitalia.com
Enter from FIUMICINO AEROPORTO
to FIRENZE SANTA MARIA NOVELLA
date: date of arrival in Rome (unless too far in the future)
Time: 00 to see all options staring from the beginning of the day. But if your plane lands at 8am, you might as well enter 08.
Most options will require a train change at either ROMA TERMINI or ROMA TIBURTINA, Rome’s main two stations. However there are two high speed trains a day that start directly from the airport and require no changes. They depart from the airport at 11:08am and 03:08pm. If you arrive just before those, they would be the easiest options. Otherwise you’ll need to change trains in Rome. There are basically a couple of trains each hour.
Unless you take one of the two direct options, you must take first the regional train to the aforementioned Rome stations. In that case you must remember to date stamp the ticket before boarding the regional train.

There is a third direct train from FCO to Florence departing in the late afternoon, but it calls at Firenze Campo di Marte and not at SM Novella.