Airport transportation in Rome

"...from the airport into the city of Rome?"

There are two major airports in Rome. Ciampino serves primarily RyanAir and has no direct rail connection, only a bus. The "main" airport, Leonardo da Vinci, or Fiumicino, is served by a train, the Leonardo Express, which goes non-stop between the airport and the main train station, Termini, in Rome. Except from about 11:30 PM until around 6 AM, it runs every 30 minutes. The trip takes 32 minutes. I believe the adult ticket price is 14€.

Another option if you want to save money (but it does take longer) is the Terravision bus from Fiumicino to Termini. This is 6 euro but takes closer to an hour.
Depending on how many people you have, it can be cheaper just to take a taxi straight to your hotel (since you may have to do that once you arrive at Termini anyway).

And another option, if you are staying in the Trastavere neighborhood or near some other stations like Tuscalana, Ostiense, or Tibutina, there is a local train from the airport to these stations for 8 euro every 15 minutes.

dana,

The quickest and easiest method is the Leonardo Express that was mentioned by Lee. There are frequent departures and it's not affected by traffic. The fare was €14 PP last time I was there, but as I recall it may be €15 PP if purchased at a staffed ticket office. That's a Regionale train so DON'T forget to validate your ticket prior to boarding the train, or you may be fined on the spot which will increase your costs considerably!

If there are several people, using a Taxi may be more cost effective. The Guidebook provides information on which Taxi's to use from the airport. You could also have a look at the excellent Ron In Rome website as that provides good information on the subject.

Happy travels!