rome to sorrento

Take the Rome to Naples Centrale station train. You'll then need to take the Circumvesuviana (local commuter) train to Sorrento.
At Napoli Centrale follow the signs that direct you dounstairs to the Circumvesuviana ticket booth. Make sure you ask which platform you'll be leaving from as not all trains go to Sorrento which is the end of the line. I believe the price is about 3 euros.
Also beware that this area is rife with pickpockets. Keep all valuables well protected at all times.
The trip from Naples to Sorrento should take about 70 minutes.

I didn't see pickpockets there (but who DOES see pickpockets) but instead there will be lots of people who want to "Help" you with your luggage. Maybe it's legitimate help with tip expected or maybe they will run off with my luggage...I just handle my own luggage and don't let anybody take it away from you.

There will also be "beggers" on the Circumvesuviana from the very young to the very old. There was a little girl who brought a violin and pretty much just sawed on the strings with her bow with no audible perception of music...her big sister was standing to the side directing her on how to ask for money after the "performance". It seems that they start training the little ones as young as possible in the art of begging.

None of these characters were dangerous - just be aware that you will see plenty of them.

thanks for your help in answering my transportation questions. It sounds like Italy has gotten really bad with the pickpockets since we were last there in 2000!