We took Ryanair from Paris to Rome and we were glad we did. We took a short taxi ride from Rue Cler to Porte Maillot (buses are parked in a lot there). You could take a subway because there is a stop nearby but we didn't want the stress of that. The bus is a nice ride through the French countryside, only takes about an hour and and lets you off right at the terminal door.
If you didn't pay online to check your luggage go to the window at the far right end of the building as you walk in the door. You will get a receipt showing you have paid.
Then, wait until you see your destination posted on one of the boards behind the ticket agent desks and line up in that line. Have your luggage check receipt ready to show the agent.
You will go through security right into the terminal area. There is a food counter and a few shops. Wait for your destination to be posted on one of 4 or 5 doors. When they post it, line up at that door.
We liked that we flew into Rome's smaller airport because it was much easier to navigate.
To take the Terravision bus to the Termini train station. Go out of the terminal and go around to the left side as you walk out the doors. You can buy tickets right before you leave the building but they sell them on the plane which took the stress off from having to find the ticket counter and wait in line.
Once you get to the Termini train station it will depend on where you are going as to which city bus to take but they are all lined up in the middle of the lot in front of the station. First, you will have to go across the street to a Tobacco shop (looks more like a newsstand) to buy your ticket. Go ahead and buy several--you will use them and they only cost 1 Euro. We tried to buy a Roma Pass there (and several other places) but they were sold out.
Hope this helps. Good luck