Rome airport to Cinque Terre

https://www.trenitalia.com/en.html

Enter
from Station of departure: FIUMICINO AEROPORTO
To Station of arrival ANY OF THE 5 VILLAGES OF THE CINQUE TERRE (Monterosso is the largest and more trains, including InterCity trains stop there).
Select date
Select time of departure (choose a time after your landing) using 24 hour clock.

All solutions will require multiple trains (at least two trains) with changes at Roma Termini (Rome's central station) and likely also at La Spezia.

Note that Rome has a dedicated airport express train from FCO that does not have to be ticketed in advance, and has an established schedule. Also remember that your plane might be late. If you are unfamiliar with European trains, you might look at our host's Travel Tips top left blue menu.

and the easiest way (that many folks recommend) to do this journey after arriving at FCO is to just walk to the ticket machines and put in those station names (usually the "from" will be there already, as you are.....standing in that station haha) and buy the next train that works best for you......it's easier than worrying about not making a train or being sad you have to kill so many hours at Termini before you get on the train you prebooked.

Agree that train, with tickets bought at the airport train station makes sense. It should take anywhere from 5-6 hours with 2-4 changes, depending on which train is chosen.

It would be helpful to follow Roberto's instructions in advance as a research project so you can become familiar with the various rail routes - there is a western route that is more direct and then a more central route that uses high speed trains to Florence, then connections to get you to the CT. For one thing, you will need to decide how many connections you're willing to make.

Better to have thought thus out beforehand rather than when you're standing at a ticket machine.

I would suggest downloading the Trenitalia app and creating an account before you travel.

Thank you all who responded to my inquiry regarding travel from Rome airport to Cinque Terre. Good tips and very useful information.
Thank you all again.
Craig