Directions for taking train from FCO airport to Civitavecchia
https://www.rome2rio.com/s/Rome-Airport-FCO/Civitavecchia-Port-Italy
Click on the train icon. Directions follow
I prefer to use primary sources.
http://www.trenitalia.com/tcom-en
It is easy. Take Leonard Express from FCO to Termini (every 30 mins) and the train from Termini to Civit.... - three to four an hour taking from 45 mins to 1 hr 15 depending on the train. Buy both tickets at the airport train station so you can walk from one platform to another at Termini. Give yourself a window of 30 minutes between trains.
There is another route taking a local train from the airport to the St. Peter's stop and catching a Regionale train to Civit.... Potentially slightly faster and cheaper But it involves more stairs and I assume you have luggage for a cruise. It is easier and simpler to go to Termini since it is flat.
If your arrival time coincides with this bus, it is probably the easiest.