Traveling from Naples to Sorrento

You can't buy those tickets online. That segment is on a commuter train, called Circumvesuviana, separate from the Trenitalia system. When you arrive at Napoli Centrale follow signs to Circumvesuviana, buy tickets at the ticket window, then go downstairs where those trains are. Validate the tickets and look for the train going to Sorrento. Circumvesuviana train timetable below:
http://www.eavsrl.it/web/en

Thank you! How much do these tickets usually cost? The price is not listed online.

Peanuts. I think about 4€ per person all the way from Napoli to Sorrento.

As Roberto said, tickets are really cheap although could be a bit more than 4€: purchase them when you arrive. The Circumvesuviana train - Napoli-Sorrento line - leaves from Garibaldi station, which is connected to Napoli Centrale. This link will take you directly into the schedule:

http://www.eavsrl.it/web/sites/default/files/eavferro/Napoli%20-%20Sorrento_0.pdf

You'll use the same train if going to Pompeii: Pompei S. Villa Misteri station is right in front of the entrance to the scavi.
This is the schedule for going from Sorrento back towards Naples (as to Pompeii from Sorrento):

http://www.eavsrl.it/web/sites/default/files/eavferro/Sorrento%20-%20Napoli.pdf

The ticket costs €3.60 for one ride on one train without stopping.
If you want to stop along the way or transfer to multiple modes of transport there is the hourly ticket for €4.50, which is valid for 180 minutes on multiple transfers.

jenny,

One point to mention is that the Circumvesuviana is rather "colourful" and has a bit of a reputation for pickpockets and scammers. It's a good idea to watch your luggage closely and wear a Money Belt.

Would it be a better idea to take a ferry? I am traveling the same route in September and had thought we would ride a ferry from Naples to Sorrento instead of the "colorful" Circumvenisia, because with jet lag it will be difficult to be vigilant.
Cynthia

The Circumvesuviana is easier if coming into Naples by rail as the transfer is right there. Otherwise, you have to catch another mode of transport across the city to Porta Beverello where the ferries leave from. The ferry schedule may also be sparse depending on time of year.

Honestly, you don't have to take any more precautions on this train than you should on any sort of public transport or at any heavily-visited tourist attraction anywhere at all in Italy. It's a bare-bones commuter train for sure but depending on how much travel you'll be doing in Italy, not the only conveyance/location requiring a firm hand on your valuables. Don't keep them in a pocket or a purse and you'll be fine.

be prepared to stand on this train from naples to sorrento too. Have been to the A. Coast a number of times and have driven to sorrento but also taken the train. The times we have taken the Circumsuviana it has been packed and not our favorite. Going from Sorrento to Naples, Herculaneum or pompeii isn't bad as it originates in Sorrento. You will just be pestered by accordian playing children, etc. On a day trip to Naples from Sorrento we took the train to Naples and the boat back to sorrento (was in month of oct. And boats running) which was much more relaxing. On our last visit there 2 yrs ago upon leaving we did a private transfer from Sorrento to Naples train station and was around 100 E. Enjoy Sorrento and the Amalfi Coast as it is beautiful!