You can travel between Naples and Sorrento by boat(ferry), along with beautiful scenery and watching Naples & Mount Vesuvius from the sea is a very different and beautiful experience. This route is slightly more expensive than the train. Going from Naples Centrale train station to the port of Moro Beverello where the ferries depart would cost you around 15 € depending on your negotiation skills with the taxi drivers and takes 15 mins max if there is no traffic. You can also take the bus from Naples Centrale train station to the port of Moro Beverello as it cheaper comparing to taxi but the bus stop does not seem to be in good location and I did not feel safe because of the ghetto neighborhood.
Alilauro Hydrofoil: The fastest way from Naples to Sorrento. It is provided by the firm of Alilauro and departs from the port of Moro Beverello in Piazza Municipio in Naples. The journey takes about 40 minutes. The one way ticket is 11 €, round trip costs 22 €.
Ferry regularly travel between Naples and Sorrento, but as the seasonal hours vary, it is always a good idea to check the departure times in advance.