Hi, There are quite a few ways to do this, and it mostly depends on where you want to go - a good option would be to rent a car and just drive, but this can be somewhat expensive. Another option is by train or bus. There are frequent services from Naples airport to Sorrento and Salerno on both ends of the coast. A third option would be a taxi or a hiring a private driver.
There is a site with much information: http://www.italytravelsguide.com/amalfi.php