I will post a primer on taking the train to Rome. You can take the free internal port shuttle bus from your ship to the Civitavecchia port entrance. From the port entrance you simply walk down the main street (keeping the sea on your left) and in 4-5 blocks (depends how you count) you will arrive at the train station on your left. We recommend purchasing a "BIRG" ticket which costs 9 Euros and will cover round trip regional trains to Rome as well as gving you unlimited use (for the entire day) of Rome's Metro (subway) and bus system (not including the HoHo buses). Do not even think about taking one of the few high speed trains since they cost a lot more, require reservations, and are not included in the BIRG ticket. You validate the BIRG ticket before you board your first train and then it will work to get you through the metro turnstyles and the Rome buses. They have now created a safe walkway within the port of Civitavecchia for those that would prefer to walk from their ship to the port entrance...but depending on docking position this can be a good mile walk (the free port shuttle buses do run several times an hour).
As to how long the train takes, it varies depending on the actual train and which Rome station. The end of the line is the Rome Termini (main station) which generally takes about 1:10..... However, if you get off at the S. Pietro staton (closest station to the Vatican) it only takes about 50 min (it takes about 20 minutes for the train to work its way through Rome to Termini). The regional trains are similar to commuter trains and have no reservations.