No need to book, just go to Roma Termini and buy ticket for €4.50pp. Remember to validate it in the little yellow box. About 2 trains an hour. This site advises times: http://www.ferroviedellostato.it/ferrovie/util/inglese.jsp. At Civitavecchia you walk along the sea front keeping the water on your left for about 10 mins until you get to the port gates where the free shuttle bus will take you to the ship. Simple.
A bit more info: the port gates actually like castle walls or a fort. As you get near to the McDonalds Restaurant , look for the Fort on your left. There is a small walkway from the street to the front of the Fort.
There is a shuttle bus stop right in front of the Fort. It is marked. The bus will have a sign on the front thats says shuttle. There may be several ships in port so ask the driver if his bus goes to your ship.