As tourism is such a major industry in Positano, there are plenty of ways to get around from place to place. 
Taxis run not only around Positano, but also between cities (for example, one could get from Naples to Positano by cab for about 100 Euros).  Trains are also available for traveling between cities at relatively decent rates.  For those who prefer to travel by sea, both ferries and hydrofoils (or “water taxis”) are widely available as well (not only for getting to and from Positano, but also for getting to and from island and coast destinations like the nearby Capri ). 

Once you are in Positano, there are several options for getting around within the city.  Car rental is possible (especially if you want to drive considerably further than just around Positano.