Train connections

Assuming you are flying into FCO airport, I'd buy a full-price ticket from FCO to Firenze SM Novella at the airport station.

Flights can be delayed and discounted train tickets can't be changed after the scheduled departure time.

The guy selling tickets at the counter will tell you if and where you have to change.
You can check the railway schedules in advance on trenitalia.com

Check train schedules at trenitalia.com You are going from Roma termini to Firenze (Florence). Lots of trains -- maybe 50 in a 24 hour period. Land in Rome -- clear immigration and customs -- take Leonard Express (local train) to Rome Termini and get on next train to Florence. You can buy all your tickets at the train station in the airport. It is easy. There are a couple of trains a day that go from the airport to Florence. You might get lucky but most likely you will need to change trains in Termini.

I HIGHLY suggest that if this is your 1st time to Europe, you need to buy & read the Rick Steves book, EUROPE THROUGH THE BACK DOOR, you can get it here on this site, but sometimes it is cheapest on Amazon -- we re-read it most every time we go to Europe. It explains things like how to use a Credit Card, how to use a Debit Card, how to get money out, how to use International phone plans, how to take a train. It is a fantastic book. The back section even has a good review of each country.

Also, look here on the site under TRAVEL TIPS - there is SO MUCH fantastic info there.

For train info, seat61.com is an amazing site.

As this is your first trip abroad, I'd agree with a previous suggestion to read Europe Through The Back Door. However as you'll be travelling in a short time, this may not be possible.

Assuming your flight arrives somewhat "on time", it will take some time to collect your checked luggage (if any) and go through Passport control. After that's done, you can make your way to the airport rail station (it's clearly marked or you can ask someone). There should be both a staffed ticket office as well as automated kiosks. The kiosks have English-language menus and are very easy to use, however you may find it easier to go to a ticket office.

You might want to have a look at the Trenitalia website to get some idea of the details of the departures at about the time you'll be travelling. You'll note that the travel time of trains on that route varies from about 2.5 hours to over 6 hours. You'll be jet lagged so a shorter travel time would be highly desirable. Note that you will have to use the Italian names of the stations. Many cities in Europe have more than one station so you'll also have to know which stations you'll be using. You'll first depart from Fiumicino Aeroporto to Roma Termini, and then to Firenze Santa Maria Novella. If you can make it, the 09:38 departure would be good, arriving at 12:01 (travel time 2H:23M). That train shows one change (Cambio) at Roma Termini.

It's a good idea to know which type of train you'll take on each leg of the trip. Often trips from the airport use the Leonardo Express but the train could also be a Freccia. The Freccia trains have a very distinctive appearance and are very easy to recognize - https://www.trenitalia.com/content/dam/tcom/it/le-frecce/1400x510_le-frecce_FR1000def.jpg . There's also the FM1 train, so be sure you board the correct one. You may find this helpful - https://www.italianairportguide.com/fco/rome-fiumicino-trains.htm#/search . The L.E. and FM1 are Regionale trains so it's VERY important that you validate (time & date stamp) locally purchased tickets prior to boarding the train, should you be using those. Failure to do that can result in hefty fines collected on the spot. Validating does not apply to tickets purchased online.

If you take the 09:38 departure, you'll be travelling on a Freccia train, which has compulsory seat reservations that are specific to train, date and departure time, so you won't have to validate the ticket but will have to sit in the assigned seats. The seat reservations specify the Carrozza (coach no.) and Posti (seat no's.) where you must sit. This video is a bit dated but may be of some help - https://www.youtube.com/watch?v=6n8rITO1Eek . When you arrive in Rome, you'll have to disembark from the first train, and then board the high speed Frecciarossa to Florence. The large electronic signboards will list the track / binario that the train to Florence is on.

You didn't provide any information on where your AirBNB is located but if it's right in Florence, you could take a Taxi from the station.

Buon Viaggio!

Dario - thanks for the feedback. I've revised my post, at an earlier hour of the evening. Hopefully this reply is more concise and accurate

but I suspect it's a direct train however the train number will change when it reaches Roma Termini.

No. Just no. When a railway site says that you have to change you have to get off and transfer to another train. Any other way of programming the site would not be logical.

If you take the 09:38 departure, you'll be travelling on a Freccia fast train all the way to Florence.

The Frecciarossa #8335 that departs from Fiumicino Airport station at 9:38 goes to Naples, to southern Italy, not to Florence.

If kimberlee followed your advice, she's end up wondering why the florentines are so proud of their pizzas and don't know where Michelangelo's David is.

By the current schedules, there is only one direct train from Fiumicino Airport to Florence, Trenitalia's Frecciarossa #9423 that leaves from the airport at 1:53 PM.

(Sooner or later Italotreno will break trenitalia's monopoly at Fiumicino, but for now there is only one direct daily train going north from the airport.)

Thank you everyone for your comments. We purchased the Florence and Rome Rick Steves travel books and have read both. Its just alot to take in having never gone abroad before. We are excited, but will feel better once we better understand the train system.

All you need to know about trains in Italy
https://www.seat61.com/train-travel-in-italy.htm

When using the trains, especially at first, DONOT be afraid ask fellow travelers for advice about where the train is going. If they ignore you, ask the next one. You will find people who are willing to help you. They may ignore you simply because they do not speak English --- but --- a lot of local people do speak some English and will be eager to help you. For us, it has been critical since it prevented us from boarding the wrong train. Also watch the departure board as the platform can change within the last 15 mins or so.