Positano

The buses run with any weather. From the airport you can take a private car transfer. It's the most convenient and fastest way but it's very expensive (€80-100 for up to 3 persons). The cheapest way is a CurreriViaggi bus from the airport to Sorrento for €10, then from Sorrento take a SITA bus to Positano (for a handful of euros).
I can't open the website of the Curreri Viaggi for some reason, but you can check the schedule below. Tickets are purchased on board.
http://www.sorrentoinfo.it/orari-autolinea-aeroporto-di-napoli-capodichino-sorrento/
For SITA bus from Sorrento to Positano:
http://www.sitasudtrasporti.it/public/tpl/campania/5070.pdf

Laurie,

I don't recall any Buses operating within Positano but I believe there are Taxis. There are Buses to get to Ravello and other locations, but I don't remember where they depart from.

If you're staying in town, walking is about the only way to get around. The town is on a hillside so if you walk down to the harbour area (such as to access the boats to Capri or the many shops and restaurants), it's going to be uphill to get back to your lodgings.

Roberto provided good directions on the options to get to Positano from the airport in Naples. Which one to choose will depend mostly on your budget. In the same situation, I'd probably take the Curreri Viaggi Bus from the airport to Sorrento, and then either a Taxi or Bus to Positano. I was able to access the Curreri Viaggi Bus schedule and they appear to have regular departures. Click on "Bus Routes" and then "Go There" in the section for Naples Airport to Sorrento.

There are buses in Positano. I took the bus to Amalfi from Positano, and it went
further south..... but I got off in Amalfi.
The bus also goes north to Sorrento.

I think Frances is referring to the SITA bus that goes from Sorrento to all the towns along the Amalfi Coast. It makes two stops in Positano, but there is no bus that I recall within Positano itself.

The Flavio Gioia bus service (orange bus) follows the lower ring road in Positano every half-hour, passing along Viale Pasitea, Via Cristoforo Colombo and Via G Marconi. Stops are clearly marked and you buy your ticket (€1) on board. It passes by both SITA bus stops. Check for any changes in the timetable when you are there.

http://www.flaviogioia.com/index.php?sez=Mappa+delle+linee&id_categoria=45&id_sezione=8&p=dx

Click on the Union Jack (British flag) top left of page to get a translation of sorts!

There is a local bus into Positano but for us it was easier to just stay on the bus from Sorrento and get off at the second Positano stop. We made the mistake the first time by getting off the bus from Sorrento and getting the local bus into Positano as the local bus was very small and we had to take luggage into bus itself which was a pain as the small bus was so crowded. The bus from Sorrento had luggage storage underneath so this was much easier. Just get off second stop. The local bus also does not go down to the harbor but stops at what I would call mid-town. Then you just continue down to harbor, etc. don't remember any cars down in the harbor area itself.

If it's raining cats and dogs, then I guess you'll stay indoors with a picnic and a good book. Weather reports are pretty easy to get online or from hotel staff.