BY TRAIN
National train to napoli central station, then take the local train "Circumvesuviana" (timetable) to Sorrento. Once in Sorrento there is a little square just below the train station take the bus "SITA" (timetable) to Nerano.

WITH BUS FROM ROME OR NAPLES
The bus from Rome (timetable) arrives in the central "Tasso" square, From here (100meters) move to the square just nearby the Cicumvesuviana station, and then take the bus "SITA" (timetable) to Nerano.
From Naples airport, Curreri bus (timetable).

FROM AIRPORT WITH TAXI O R BUS
From the Airport (website) you can take a taxi and  go  the main railway station and then take a train to Sorrento, or you can go to the port  (molo beverello) and with a hydrofoil  you will be in Sorrento in just 30 minutes. Should you arrive after 10pm will be highly recommend to arrange a private transfer.
From Naples airport with bus, Curreri bus (timetable).

BY HIDROFOIL
From molo beverello (in the port of Naples) you can reach Sorrento in just 30minutes by hydrofoil. (website). From the port move to the square just nearby the Cicumvesuviana station, and then take the bus "SITA" (timetable) to Nerano.