Options for transfers from Naples (not sure if you are coming from the train station or airport) to Positano and Sorrento:
- Circumvensuviana train to Sorrento, bus or ferry from Sorrento to Positano and back.
- Taxi or shuttle to Port of Naples. Ferry from Port of Naples to Positano. Any of above options to Sorrento from Positano.
- Private driver (pre-arranged) from Naples to Positano. (best if arriving in the evening) Any of above options to Sorrento from Positano.
If you are trying to reach Positano from Rome and don't really want to spend time in Naples, you may want to consider the bus that goes 2x daily from Rome to Sorrento. This saves several transportation connections.
Once in Positano you can enjoy the town or take the bus or ferry to one of the other Amalfi Coast towns for a few hours. Capri would be best reached by ferry from Sorrento (about 25 min./ 13.50 euros each way) rather than using one of your days in Positano. Pompeii is reached by Circumvensuviana train from Sorrento. You can pick up a tour there at the ruins or arrange it through your hotel. You may consider doing Pompeii on the day you depart from Sorrento since it is on the way back to Naples for most transportation connections.
Have a wonderful trip!