Transportation from Rome Airport to Sorrento

Train from FCO to Rome Termini. Fast Train (Eurostar) from Rome Termini Naples. Commuter train (Circumvesuviana) from Naples to Sorrento.

And the nice thing about the switch in Naples is that you don't even have to leave the train terminal to switch from the Rome train to the Circumvesuviana. You just go to a different part of the station. (Be sure to ask what the track number is for the Circumvesuviana train that goes to Sorrento. I seem to recall that there are three or four separate train lines on the CV.

If you're planning on visiting Pompeii or the Archeological Museum in Naples, I'd recommend getting the Campagnia Arte Card. It comes in several versions, but the one you want costs 25E (as of now) and is good for 3 days unlimited rides on the Circumvesuviana train and transportation in Naples, free admission to 2 museums or sites, and 50% discounts on further sites. You can find more info on the web. Best of all, they sell it right at the Naples train station. We bought one when we got off the train from Rome, then walked downstairs and used it to get on the Circumvesuviana to Sorrento.