Trastevere Taxi

The tram runs on Viale di Trastevere. The easiest public transit option to the airport is tram to Trastevere train station and then the regional train to the airport (at least 2 per hour). There are taxi stands at the Ponte Sisto (to the left as you face the bridge) and on Viale di Trastevere just before it crosses the Tiber (in the small piazza with the statue). There are almost always a few taxis waiting at those 2 locations.

From 5:20 onward every day, you can catch a direct train to Fiumicino airport from Roma Trastevere train station, marked on a variety of maps.

Otherwise, if you're staying at a hotel and need to depart early, they will book a taxi pick-up to take you to the airport.

Black & white maps in Rick's book show taxi stands as a T in a white circle and tram stops as a T in a black square (legend on p. 2 of Italy book).

The Trastevere train station is a little gritty looking but don't let that discourage you. If you don't want to deal with either the ticket window or the ticket kiosk (often there are lines), you can easily buy a ticket to FCO from a human being at the news kiosk inside the station. It's to your right as you enter the station. You'll have to walk right by it to get to the underground passageway out to your platform.

Where are you staying exactly in Trastevere? It's a very large district.