what is the fastest and most econimical way to get from cruise port in Naples to the amalfi coast
You can ride the Circumvesuviana train to Sorrento and then the SITA bus to Positano and Amalfi. Or take the ferry or hydrofoil to Sorrento and either continue by boat or bus. If you only have a day though, I would consider a private driver like Romeinlimo or any of the other many companies that make that route. Not the cheapest by any means, but you would see the most.
My wife and I took ferry (hydrofoil) from Naples to Positano. Nice little trip.
Actually the Circumvesuviana train to Sorrento, where you pick up the bus at the train station (make sure to buy your tickets from the kind, elderly couple who operate the shop in the station) and it's actually really cheap. Make sure to sit on the right side of the bus, and enjoy!