Get the shuttle bus to the harbour entrance, walk along the sea front a few hundred yards, and get the train to Rome. It's about an hour to St Peter's Square - we advise getting off there as it takes about 20 minutes around the city to get to the central station.
At St Peter's there's the Vatican, Sistine Chapel and the famous square. Then cross the River Tiber and see the sights of the city - Spanish Steps, Forum, Trevi Fountain and Colosseum, with history all the way. Be prepared for big queues to get inside the Colosseum.
You can arrange your route to end up at the central station - note that the platform for trains to Civitavecchia is about 10 minutes walk from the station entrance.