Getting from Rome to Sorrento

Marina, I recommend taking the train.

Take a train (Trenitalia or Italo) from Roma Termini to Napoli Centrale, walk through the station to the adjoining Napoli Garibaldi station and purchase tickets for the local Circumvesuviana train, Naples- Sorrento line:

http://www.eavsrl.it/web/sites/default/files/orariautomobilisti/NapoliSorrento_New2015.pdf

You'll want to remember to validate your tickets before boarding the train to Sorrento.

Marina,

I agree with Kathy. Take the train Termini to Naples Center. Be cautious in Naples station, there are shady characters looking for easy pickpockets. Then the regional train to Sorrento. The regional train can be crowded depending upon the time of day. Remember the locals use train for work commute. From the Sorrento station there are taxis, or walk a few blocks to the bus. What is your final destination?
Lorieann

Thank you both. We'll definitely take a train.

We decided to have Sorrento as our base for 6 days to explore South of Italy. We'll spend the last night in Naples just because we are flying back from Naples.

Any recommendations on the day trips from Sorrento will be very welcome.

Thank you,

Just to add another option you can take the train to Naples then a taxi to the port. If the weather is nice and the seas calm the ferry to Sorrento is much more enjoyable and secure than the train. Also you'll enjoy the views of the coastline and Mt. Vesuvius.
As for day trips there are many fine options. The Amalfi Coast is a must see. You can hire a private tour which although more expensive is more flexible with stops for photos. There is also ferry service from Sorrento to Positano and Amalfi as well as buses.
Consider a trip to Pompeii. It's a 30 minute train ride from the Sorrento station.
A day trip to Capri is also worthwhile. The Blue Grotto, the chair lift to the top of the island and Villa San Michele are just a few of the attractions.
RDJ

Marina,
I would take a day trip via local bus or train to Pompeii, plan on spending the entire day take the return trip back to Sorrento early evening and have dinner there. Also a day trip to Capri. Take a ferry from Marina Grande to Capri. Before booking the tour be sure the tide isn't too high or the wake not too choppy because the smaller row boat won't be able to enter the grotto. The tour companies don't tell you that you won't be able to enter unless you ask. The entire island can be visited in a day. It's very expensive but the views are breath taking. Also take a bus to Amalfi and from there you can take a smaller local bus to other towns such as Positano or Ravello. Ravello you can see in a few hours. Also take a day to just stay in Sorrento and enjoy the lovely town my favorite!

Lorieann

Marina,

The cheapest method will be to take the high speed train from Roma Termini to Napoli Centrale, and then go downstairs to the Garibaldi station and buy a ticket for the Circumvesuviana commuter train. That will get you to Sorrento in about an hour. The Circumvesuviana is not the most "desirable" option as it has a bit of a reputation for pickpockets and scammers, but it will get you to Sorrento. You'd also use that to get from Sorrento to Pompeii. If you decide to take the Circumvesuviana, be sure you're wearing a Money Belt and watch your luggage closely.

A more expensive but much more comfortable method is to again take the high speed train from Rome to Naples, and then arrange for a private car service to take you to Sorrento. The Monetti Taxi listed in the guidebook is a good choice.