Rome Airport (FCO) to Florence

Here you go: http://www.trenitalia.com/tcom-en

Note that even in the English version, you need to insert the Italian station names (Fiumicino Aeroporto to Firenze).

There are some direct services, but also more frequent services that have one change at Rome Termini, and don't take much longer. Certainly take the Leonardo Express from FCO (not the regionale service) if you do select the one-change option. All is revealed on the site.

Great, thank you. It seems that the train is the more efficient way to go.

Note that fares can be significantly cheaper booked online well in advance (up to 90 days), but you lose flexibility.

There is also the alternative company, with cheap fares from Rome Termini to Florence: https://www.italotreno.it/en

You will nearly always need to change,but it still faster than changing to another plane at Fiumicino airport.

Contrary to Jingli, you may well find the trenitalia website advises you to use the regional train from the airport to Rome Tiburtina and change there for Florence. Unless you are piled high with baggage, there's no reason to avoid using this commuter line from the airport.
And in Florence, just make sure your train goes to Santa Maria Novella (SMN) station in the city centre. Nearly all do, but just a few only stop at other stations in the suburbs.
I always point out too that the staff in the ticket office at the airport speak some english and deal with hundreds of international passengers every day. If you decide not to book your tickets in advance, the staff will be good at sorting out your journey when you arrive at the train station in the airport

I suppose you checked whether you can book a flight from your home town to Pisa airport.
Once at Roma Fiumicino airport, Venice Marco Polo airport or Milano Malpensa airport, it's easier to reach Florence by train, indeed.

Well, you can catch the slow regionale train to Tiburtina, but there is no advantage in doing so, and it just unnecessarily muddies very clear waters. They are no quicker, and can be a lot slower.

Catch one of these:

• Leonardo Express to Termini, then Freccia to Firenze SMN
• Non-stop Freccia from FCO to Firenze SMN

The non-stop might also save you the fixed cost of the Leonardo Express. And while you can buy tickets on the day, it can be insanely more expensive than if you book in advance. For example, check fares for tomorrow versus 8-10 weeks hence. And fares can vary widely over the day too.

It's all down to your particular arrival time as to how long you need to wait for connections by air or train. Either may also be more convenient than the other depending on your plans in Florence and after. If you have luggage then air is convenient as you'll likely have it automatically transferred and won't have to lug it on and off trains.

Bear in mind that if you make seat reservations on a premium train your tickets are useless for any other train. The fast trains from FCO to Florence are very frequent, I personally would buy tickets on arrival.

The fast trains from FCO to Florence are very frequent, I personally would buy tickets on arrival.

Umm ... as I've already stated, the direct service from FCO to Florence are fairly infrequent (every four hours or so), but there are a lot of services that run from Central Rome, after you've caught a train into town.

If you want the option of being able to catch the next available train relative to your landing and clearing all processes, then yes, don't purchase a ticket in advance, and pay a premium for flexibility on the day.