From Naples’ Capodichino airport, take the specially-marked Alibus (3 Euro ticket, purchased onboard) to the Napoli Centrale train station at Piazza Garibaldi. Be sure to validate your ticket in the onboard box.

Alternatively, a taxi from the airport to the train station can be hired for 16 euro. This is a fixed fare. Let the driver know you want the fixed fare BEFORE you get into the cab. More information is here including a link to all Naples' taxi fares and fixed fares.

If you elect to take the bus you can either pay the driver or purchase a ticket in the sundries shop just inside the door. Not sure if only one terminal, but the bus was outside just past the McDonald's at the far end of the terminal with the outside on your right.