Naples International Airport: There is no rail link to Positano. In season, a pre-booked direct airport coach is the sensible public-transport choice: roughly 1 hr 40 min and about €45, but schedules are seasonal. For a cheaper, more flexible route, take the airport Alibus to Napoli Centrale, continue to Sorrento by Circumvesuviana/Campania Express, then take a ferry to Positano when it is running; allow 3–4 hours door to door and do not attempt it late in the day with luggage. A pre-booked private driver is expensive (roughly €150+), but is the least miserable answer for a late arrival, children, or several bags.
Napoli Centrale / Piazza Garibaldi railway station: For public transport, go to Sorrento by Circumvesuviana (cheap but crowded and poor with large luggage) or the more comfortable Campania Express when it operates; then use the seasonal Sorrento–Positano ferry, about 40 minutes, or the SITA coast bus, about 40 minutes in clear traffic but frequently longer. Budget 3–4 hours from train platform to Positano hotel. Do not confuse this with a straightforward rail transfer: Positano has no station.
Sorrento: The ferry is the good option in sailing season: around 40 minutes, scenic, and it avoids the jammed Amalfi Drive. Use the SITA bus only when the sea is rough, the ferry timetable does not work, or you are staying near Positano’s upper road; it can be packed from late April onward. On the bus, sit on the right from Sorrento for the views.
Salerno railway station / ferry port: Arrive by fast train at Salerno, walk or take a short taxi to the port, then use a seasonal ferry to Positano. It is usually far calmer than crossing the peninsula by road; allow roughly 70–90 minutes on the water plus the station-to-port connection. If ferries are not operating, the SITA coastal bus is cheaper but slow and vulnerable to traffic.