There is no train to Positano. The options are bus, ferry, or car — and if you drive, you will still need to walk the final stretch.
SITA buses run the Amalfi Coast road continuously in summer, connecting Positano with Sorrento (about 1 hour) and Amalfi (about 40 minutes). The road is spectacular but narrow and slow — book a window seat. Buses stop on the main road above the town, from where a smaller orange bus runs down to the waterfront.
Ferries connect Positano with Naples, Amalfi, Sorrento, and Capri. In summer, hydrofoils run regularly; in winter, services are reduced. The ferry dock is right on Spiaggia Grande.
If you arrive by car, you will park above the town (expensive and often full in summer) and walk or take the local bus down. Positano has no through road for private vehicles within the lower town.