This port is called Civitavecchia. The harbour provides free shuttle buses to the city. From the bus stop you can walk in 15 minutes to the train station where you can get on a cheap train to Rome for 7 euros in 70 minutes or you can take a quicker and expensive train.
Awfull. The ship docks very far from the city. The taxis are extremely expensive. The shuttle bus was 7 euros per person and took 30 minutes and 20 minutes waiting time to get to the uninteresting city. Stay on the boat!