train

Follow the signs for the train to Rome - Leonard Express. At the ticket window buy a ticket to Rome Termini (validate the ticket in the yellow box) and buy a ticket to Naples from Rome at the same time. Give yourself about 30 to 45 minutes between arriving in Rome and the departure to Naples. And go to Naples.

Nick, What Frank said. A few additional comments. If this is your first trip to Europe / Italy, I might allow a bit more time for the connection at Termini. It's often somewhat busy and chaotic, which could be intimidating for those not used to it. When you purchase your rail tickets at FCO, you can use either the staffed ticket offices or the automated Kiosks (credit card required). DON'T forget to validate the tickets in the yellow machine. The Leonardo Express arrives at one of the outside tracks (Binario 26 as I recall), and you'll need to walk to the other end of the station to locate your train to Naples. Your trip to Naples will likely be on a EuroStar Italia / Alta Velocita / FrecciaRossa train, with reserved seats. Your ticket will specify a Car No. (Carrozza) and a Seat No. (Posti). Note that tickets with reservations are specific for a particular train, so if you miss that one you'll have a problem. If you're caught without a valid reservation for the train you're riding on, you'll be fined on the spot and it won't be cheap! The train number will be shown on the ticket (ie: Under "Numero Treno" is will state something like "9509 FrecciaRossa" or whatever). Will your Son be meeting you at Naples station? Happy travels!

thank you Frank and Ken for your input!