Simple and best way to figure out the illusive boat schedule between islands and coastal towns of Sorrento, Amalfi, Positano, et. al., is to visit the ticket office. Metro stop Municipio on Line 2 gets you there - take the Porto exit and walk right.
What they don't explain very well is where to get on the boat. There are multiple boat companies, and they dock at one of two docks... which resulted in my friend and me getting our inadvertent morning run on.
To Sorrento we went! And from there we boat-hopped to Amalfi, then Positano. This day was one of the highlights of our trip. We only spent an hour or so on each island, but we loved every minute of it. Our route starting at 10am from the port of Napoli consisted of: boat Napoli-Sorrento, boat Sorrento-Amalfi, bus Amalfi-Positano, and bus from Positano to one of the train stations.
A word of warning: the evening buses back to Naples (or to train stations that get you back to Naples) are CROWDED so make sure you 1) buy the bus ticket as soon as you arrive at the island, and 2) have plenty of time to miss a bus; even if you get to the station, the line of people in front of you may cause you to have to cram into the bus after the bus you think you're waiting for. read more