Transportation from Naples to Positano

The easiest solution (although not the cheapest) would be to hire a private driver for that trip. You might have a look at this firm, which I believe is still listed in the guidebook - http://www.monettitaxi17.it/English.htm . Send them an E-mail for an estimate.

Not sure if you know already that from Naples most either take the Circumvesuviana or Campania Express trains to Sorrento and then a bus or taxi or ferry to Positano. There can be a lot of car traffic on the auto route.

Honestly I was on the Amalfi Coast yesterday and would strongly advise against driving to Positano. The road between Sorrento and Amalfi is extremely narrow and windy, often cars would have to stop and reverse back up the road in order to let buses get through.

A better option is to catch the Circumvevusica train direct from Naples to Sorrento. When you get off the train, in Sorrento, there are tour operators selling bus tickets to Positano (Sita bus) which are very reasonably priced. Alternatively you could walk through Sorrento to the boat jetty/beach area and catch a ferry to Positano.

Some people have mentioned pick pockets on the train but I didn’t experience that at all (as a 30s solo female traveller), I found all the locals very friendly and helpful. But the train does get very busy during peak hours.

A better option is to catch the Circumvevusica train direct from
Naples to Sorrento. When you get off the train, in Sorrento, there are
tour operators selling bus tickets to Positano (Sita bus) which are
very reasonably priced.

This is the cheapest option. Train to Sorrento and ferry to Positano is the next least-expensive option. There are no direct ferries from Naples; if wanting to go by water, I'd suggest train to Salerno and a ferry from there to Positano. There are also ferries from Sorrento but they run to Positano more frequently from Salerno.

Find bus and ferry schedules here:
https://www.positano.com/en/ferry-schedule?from=salerno&to=positano#