There are a variety of convenient ways to get from Rome to Sorrento. The most convenient option is to rent a car and to drive across the A1/E45 (3 hours), but those uncomfortable taking the wheel on Italy's roads have a variety of other ways to get there.
Many choose to take a high-speed train from Rome to Naples, and to then take a private transfer, the quickest option (2 hours total). For a more scenic experience, you can replace the private transfer with a ferry, but do note that the port is over a mile away from the train station in Naples.
Besides a car, a bus from Rome to Sorrento is the only direct option without any transfers (3.5 - 4 hours).
Before heading to Sorrento, make sure to check this Relaxed 7-Day Amalfi Coast & Rome itinerary for neighborhood and market recommendations.
Duration: 3 hours (more with stops and traffic)
This is the most convenient way to get from Rome to Sorrento, taking the A1/E45. To get to Sorrento, take the Castellammare di Stabia exit (do keep in mind that, contrary to popular belief, the exit is not called Sorrento). Initially, the drive is not particularly scenic. Once you exit and are on the SS145 the streets begin to become narrower, the traffic becomes notoriously congested, and besides the three tunnels you'll pass through, the views will become more impressive; there are various panoramic photo opportunities between the Castellammare di Stabia exit, the towns of Meta, Piano, and Sant'Agnello that you will pass through, and Sorrento's center. Though the drive is not exceptionally difficult, for those taking the route for the first time, it is recommended to make the trip before the sun sets.
Two convenient detours you could make are Naples and Pompeii. If you plan on extending those detours into multiple days exploring the Pompeii ruins and Mount Vesuvius, make sure to check this Naples & Amalfi Coast itinerary.
By Train and Private Transfer or Ferry
Duration: 2 - 2.5 hours
There are two train operators to choose between, Trenitalia and Italo; both run direct, high-speed routes from Rome to Naples. Taking the train from Rome's Termini station, the ride to Naples' Napoli Centrale station is a little over an hour. Should you be starting the trip at the airport, you would need to take the Leonardo Express train to Termini and transfer as there are no direct trains to Naples from Rome Fiumicino Airport. Though it is possible to purchase tickets directly at the station, during the summer season seats for the high-speed trains can run out quickly. The earlier you book the better, and all tickets are available online.
Once in Naples, you have various options to select from. The most convenient but also the most expensive option is to take a private transfer all the way to Sorrento (1 hour). Another option is to take a high speed ferry from Naples' Molo Beverello port direct to Sorrento run by operator Alilauro (40 minutes) but the port is 15-minute taxi ride away from the station which might be inconvenient for those with large luggage, and the destination port Sorrento is a steep climb away from the city center (the ferry, however, could be an exciting experience).
You can also take a bus from Naples to Sorrento, run by private companies depending on season. The least convenient option from Napoli Centrale to Sorrento is the Circumvesuviana commuter train (1 hour 10 minutes) since trains are often canceled, there is no air-conditioning nor luggage racks, and tickets are not purchasable in advance online.
Duration: 3.5 - 4 hours
This is a direct route from Rome to Sorrento with bus operator Marozzi or Europe's low-cost bus operator Flixbus and is the most affordable way to get from one city to the other. It's an especially convenient option as it requires minimal transfer of luggage between modes of transportation. The downside, however, is that there are only four available trips per day in total between Marozzi and Flixbus. During the summer season, it is necessary to buy the ticket online in advance as seats run out quickly.
Take either of the buses at Rome's Tiburtina station for a 3.5-4 hour ride scenic ride. With Flixbus, the destination is Sorrento's Corso Italia 259, whereas with Marozzi, there are four drop-off options within Sorrento: Chiesa Madonna del Lauro, Bar Siesta, Piazza Sant'Agnello, and Corso Italia 259.