It's much easier to get tips on how to spend money while traveling, than how to save them during your trip. That’s why I'd like to share with you some tricks about saving on public transport in Naples that you might find useful. Also, these are typical public transportation ways that the Neapolitans are using, so it will let you learn more about the locals while fitting in.
First thing: Taxi or bus in Naples?
You just landed in Naples, don't have a mountain of luggage or you are not in a big group with which you could split the taxi cost. Take the special bus from the airport! You don't have to book before and you can buy the tickets directly on the board. Just in front of the airport, there is a bus stop which is bringing you for only 4 euros to the central train station, port or the main square. The taxi costs from about 20 euros fixed tariff and unless you're not in a big group or having too heavy luggage I'd suggest that you take a bus instead.
Take the Naples metro
Not only you can visit, according to BBC, the most beautiful metro stop in Europe: "Toledo", but also it's a 1 euro cheap way to give your feet a break. If you think you will move a lot with the public transport inside the city I suggest that you take a 3,50 euro daily or 12 euro weekly ticket. All the public transport, like bus, metro, and funicular, which move inside the Naples are included in the ticket.
Visit Hercolaneum, Pompeii and Sorrento with public transport
One of the coolest things about Naples is that you can travel to some other very cool places like Herculaneum, Pompeii or Sorrento super cheap and you're not obligated to look for the special buses or book anything, an easier and cheaper way exists. There is a train that leaves right from Garibaldi central train station. It's called "Circumvesuviana". You can get the tickets near the entry and the price is only from 2 to 3 euros, depending on where you want to go. And it takes only about 20 minutes to go to Herculaneum, 40 minutes to Pompeii and 1 hour to Sorrento.
Hope you'll find these tips useful for your journey in Naples. Use public transport in the cheaper way and use the money you save for something more exciting.
So, use the public transport, save money and visit Naples.