Stazione FS Fiumicino Aeroporto

Compared to the barely controlled chaos of some of the Italian train stations (the main train terminal in Rome [the Stazione Termini], for example, ON A GOOD DAY has all of the ambience of a big box store’s Black Friday sale — complete with rude crowds and confused people, plus add in a Tower of Babel for fun, pickpockets and other assorted ‘pond scum’ — yeow!) this terminal, on the other hand, is an island of order and tranquility that has fast trains to downtown Rome.
Use the red ticket machines or the helpful people at the booths to buy your tickets. English is fine for both.
You can even get trains from here to Florence or Venice. Just remember to time punch your tickets at the green validation machines before boarding. Reportedly forgetting that step can end up costing you $$$ in fines.

For any travels between the city and airport, be sure to book the train for Leonardo Express for timely, fast transportation. This station is pretty easy to navigate and understand when and where to go for the terminal, providing the information in multiple languages to assist all foreigners.
However, if you’re running late to your flight, there is a good amount of distance to cover before you get to the airport check-​in area, so be sure to book a train that gives you plenty of time to walk from the station.

Schneller Weg vom Terminal 3. Übersichtlicher Bahnhof. In der Mitte der Leonardo Express zum Termini. Am Rand die langsameren und preiswerteren Züge zu den anderen Bahnhöfen.

As train stations go, this one is well-​organized and quite convenient. It is a quick walk across a sky bridge from terminals 1,2 and 3 at the airport. The station is fully covered in case of rain, and there are convenient ticketing machines, as well as a well-​staffed ticket desk.
From here, you can get the Leonardo express train straight into Rome, every 30 minutes, as well as several local trains to other locations, including Rome Tiburtina station, which is where many of the high speed trains on the Italo line to major cities depart from.
This station is one of the best organized features of this otherwise chaotic airport.