The airport of Naples is called Capodichino and is located not far from the central train station and the city center. From the central station it is very easy to reach the most beautiful parts of the city by bus and metro (and even walking).
Public transportation Naples
To/from Naples
Capodichino Airport
Almost everyone calls the international airport of Naples is called Capodichino by almost everyone but is officially called Aeroporto di Napoli Ugo Liutta. It is located about 6 kilometers outside the city itself. It is easy to get to the center by bus.
Central station

Naples’ central train station is called Stazione Centrale and is located at Piazza Garibaldi. The street south of the station is called Corso Lucci, while the street on the north side is called Corso Meridionale. There is a metro stop at the station, and there are also several bus lines to the center.
Public transportation within Naples
Metro
There are only two metro lines in Naples. It is best to buy the tickets beforehand, since the machines are often out of order. Note that different tickets have to be used for each line.
Regional train Montesanto station

From the Montesanto station there are multiple railway lines to the outskirts of the city and beyond.
The Ferrovia Cumana railway line connects the station to Pozzuoli. There are stops in the suburbs of Fuorigrotta, Bagnoli and Baia. The last stop is in Bacoli.
The Circumflegreia line follows a different route but also connects Montesanto to Bacoli.
Taxi
In Naples, as everywhere else in Italy, there are rules for how much one may charge for a cab ride and, as elsewhere in Italy, these rules are often not followed. In addition to the normal time- and distance-based fares, there are fixed prices to and from the airport and the Molo Beverello port.