Assuming your point of departure is NAP airport, you have two options:

1. From NAP hop on "CURRERI" bus to Sorrento (abt 1,5 h time) and from Sorrento SITA bus to Positano.

SITA Timetable: http://www.sitabus.it/sitabus/campan...A/QUADROXV.pdf

2. From NAP city bus (Alibus) to Naples railway station.
Train to Salerno
From Salerno station, walk out to marina port (5 min. - just opposite -) and
catch a ferry to Positano: http://www.salernostazionemarittima....-positano.html

3. As the option n.2, substitute train with bus from NAP straight to Salerno: http://www.buonocore-group.it/tratte...li-capodichino

And then follow by ferry Salerno-Positano (which also stops in Amalfi)

Choice mostly depends on your arrival time.
Enjoy the Costiera!