The SITA SUD buses and the Trenitalia trains connects all the Campania areas. They will be your best friends, especially if you are not traveling by car.
In Napoli you can take the underground train too. Moreover, there are three more railway lines: the Circumvesuviana line that connects the city centre with the Vesuvius area up to Sorrento, the Circumflegrea line that connects the city centre to the western Flegrea area, and the Cumana line that connects the city centre with the eastern Flegrea area.
Salerno has an underground train line too. The underground stops at the most interesting areas of the city.
Salerno and Napoli offer maritime transports as well. The Metrò del Mare ferry boats connect the two maritime cities with the most important town of both the Amalfi Coast and the Sorrento Coast.