If you are in Rome and wish to visit Positano, I would say you need at least 2 days available for this trip. It could be done in one day but you would have to take into account that all the time you will spend getting there and returning, won´t leave much time to actually enjoy some quality time in Positano.
Here are some options you can take when planning your visit to Positano from Rome:
Train from Rome to Naples and then to Sorrento. Followed by Hydrofoil from Sorrento Port to Positano.
“Trenitalia’s Alta Velocità” (AV) trains make the trip from Naples to Rome 87 times per day. The first train leaves Napoli Centrale bound for Roma Termini at 4:04 a.m., the last at 9:46 p.m., the trip takes an average of 1 hour and 7 minutes. Ticket prices on this route range from USD 26-40.
The Train from Naples to Sorrento takes 1 hour and 10 minutes and it runs about every 20 minutes. The cost is about 4€
Once in Sorrento you will have to take a Taxi from the Circumvesuviana Train Station to the Port to catch one of the Hydrofoil Boats going from Sorrento to Positano. Prices start at 15€. Trip duration is 40 minutes.
Train from Rome to Salerno and then Hydrofoil from Salerno Port to Positano
Frequent Trains from Rome to Salerno. Trenitalia’s high-speed Alta Velocità (AV) trains, connect Roma Termini with Salerno several times each day, and the fastest trains make the journey in 1 hour 25 minutes. Prices vary from 36 to 50 USD
Once in Salerno Port “Molo Manfredi” you can travel with one of two companies that do the route Salerno – Positano.
By June 2019 it only shows 2 routes available from early in the morning with TravelMar and one daily with NLG.
For NLG check online Timetable and prices:
Ship Crossing Type: Fast Jet Line. Crossing Time: 50 minutes
For TravelMar check Online Timetable and prices:
Crossing Time: 1 hour 10 minutes
2 hours by car from Rome to Napoli. Plus 1 and 15 minutes from Naples to Positano. You could do it by renting a car but we wouldn’t recommend driving on Italian highways much. Hiring a Private Service could be expensive, around and more than 400€. If you are not a big fan of train rides, but still you don´t have that much budget for a private ride from Rome, the best thing to do would be to take the train from Rome To Naples (around 1 hour and 10 mins depending on the Train) and then get a Taxi from Naples to Positano. We found one taxi ride for 110€ right from our hotel in Naples to the closest to the hotel in Positano.
For a cheaper budget check out the options with Train and bus from Naples and Sorrento…