One option (besides public transport) is to rely on what are now called in Italy 'Auto Blu'.  These are simply chauffeur-driven cars that you can book in advance for your airport or station transfers. Ask your hotel to arrange a transfer for you, and you may avoid some of the hassles and overcharging. 

CMC World Travel are capable of planning transfers along the cruise path from Rome, Florence, Naples, Bari, Venice and Sicily.  

Or you can contact the typical local Italian blue car companies:

http://www.naplesairporttransfer.com 

http://www.holidaytaxis.com/

http://www.shoretripnaples.altervista...

http://www.eurolimo.it

http://www.resorthoppa.com/ 

For the licensed taxis in Naples (white vehicles, with a city badge and their registration number on both front doors), a link to the new rates - effective from April 2013 - can be found by looking for the word "english" on this page of the city comune's website...

http://www.comune.napoli.it/flex/cm/p...

  ... but do also be sure to read this essential advice from the licensing authority:

 http://www.comune.napoli.it/flex/cm/p...

Getting a driver to accept the fixed rate may be challenging, but there are plenty of taxis. If one driver refuses, ask another driver. Taxi drivers in Naples will occasionally try to charge you more if they know you're a tourist, so be aware and know in advance what a typical fare would cost for your destination.

If going to a hotel, make sure you ask front desk staff what the proper fare should be.  Then make sure the driver takes you right to the door of the hotel (they often try and drop you off at the end of the street so the hotel staff can't see them ripping you off).  Then get them to unload your bags and get OUT of the taxi before you pay.  Pay them exactly what the hotel staff told you the fare would be.  Don't take any excuses about heavy traffic etc.  If they want a big argument, just suggest that you ask the Hotel Manager to come out and resolve the matter.

When you get into the taxi note the published fares, write down the taxi number, the driver number, the telephone number on the taxi, and make sure the meter is running. There is also a tourist telephone number you can call to report the driver.

The best advice about rental cars in Naples...just avoid it. Erratic driving, heavy traffic, lack of parking, toll roads, and poor signage can lead to a very stressful experience for the average tourist. If you insist on renting a car, local & international chains offer pickup at Capodichino airport and outside the main Napoli Centrale train station. Use a GPS system to assist with directions and avoid leaving anything of value inside a parked rental car!

Picking up a rental car at the NAP airport is easy and safe.  Even at the early morning hours, it is well lit and with other travellers around.  It is about an 8 minute walk to the rental car area, which services all of the main brands.  Be advised that they do not open until 7:30, but you can go early to stake out your place in line (Hertz appeared to be open a little bit earlier).  It is easy to return the rental car after hours (if you have an early morning flight).  The lot is monitored by a security booth that is open 24/7.  Your rental car agency can confirm the instructions, but you usually leave the contract and the keys in the drop box.   There is easy access to the A1 from the lot.