The suburban rail line (FR5) runs from the port to central rome. It is pretty much like a glorified subway/metro train. It actually has a stop right by St. Peter's. Once in Rome, you can also use the metro to get to the major sites like the Forum. The train runs pretty much on the hour from just outside the port and takes about 50 minutes - you can get the exact times on the Internet.
If you know the city, this coupled with the metro can be the way to get around quickly and avoid some traffic. Note that the trains can really crowded as well and you may find yourself standing.