We arrive in Naples around noon time - looking for easiest way to get to Positano.
There is a direct bus from the Naples airport to Sorrento. From Sorrento you can then take a bus or taxi to Positano. There are also numerous private drivers you can hire that will take you directly from the airport to Positano, but they aren't cheap.
Your target price for a private transfer is about 100 euro, you may be lucky and find something for less. Tripadvisor has lots of recs for companies. Airport bus to Sorrento current timetable http://www.curreriviaggi.it/ Bus Sorrento to Positano current timetable. http://www.sitabus.it/sitabus/campania/orarioCAMPANIA/QUADROXV.pdf I would not take a public taxi service from Sorrento to Positano, IME they are some of the most expensive in Italy! A 20 minute ride in May cost us 15 euro in Bologna, last November a 10 minute ride in Sorrento cost us 17 euro.
I agree with Tom, the easiest way would be a private driver. We have used Antonio Prudente 3 times and I highly recommend him. He speaks excellent English, is reliable, honest and very nice. His email address: [email protected]