Instructions from Civitavecchia port to train to Rome
When you come out of the port entrance you will cross the street (you will see a newstand on the other corner) and turn right and walk this street parallel to the coastline for about 4 blocks and then you will be at the train station. It is quite convenient.
Street names: Walk along Calata Cesar Launrenti and it will turn into Viale Giuseppe Garibaldi. Train station is parallel to this on Viale della Repubblica.
Ask to purchase a B.I.R.G ticket and this allows you unlimited train for 24 hours and buses and metro in Rome. Cheapest way. I didn't see this offer on the automated machines so you might want to to go ticket counter.
Again, don't forget to validate ticket before going on the train in machines.
If you plan to start at St. Peter's then get off at Roma S. Pietro station and not the main TERMINI station.
Note: We were in Rome on a sunday so when we arrived at main Termini station at end of day it was a bit confusing as we didn't know that on weekends some trains don't run so we ended up having to catch another train 30 minutes later. The confusing part is it didn't have "Civitavecchia" as the end station but ended up having "Firenze as is Florence" on it but it stopped in Civitavecchia. So, if you are in Italy on Sat. or Sun. make sure you check the return train times before you go to see the city. It is in small print on timetable indicating about not running on weekend.
Also, watch out for major pick pocketers in Rome train station. There are women and men who offer to help you and then want money as well.