Hey Val,
There are four ways to get to Pozzuoli from Naples:
The underground subway
The Cumana commuter rail
The EAVBUS
Naples City Bus no. 152
Which method you take will depend largely on your departure point in Naples.
If you want to visit the Solfatara Sulphur pits, Naples City Bus no. 152 stops at the front entrance.
You can get to Pozzuoli, on ANY of the 4 foregoing operators, with an UNICO NAPOLI ticket for 1.10 Euros. It's good to buy your return ticket as well, so as not to hunt down a sales outlet in Pozzuoli.
The Campi Flegri is about a 15 minute walk from Pozzuoli.
Solfatara - The park is 10km (6 1/4 miles) from Naples. The easiest means of travel is the Metro (line 2) to Pozzuoli-Solfatara station, which is only about 732m (2,400 ft.) from the entrance to the park. You can walk the distance or catch the local P9 bus from outside the Metro station. City bus no. 152 from Naples to Pozzuoli also stops at Solfatara.
Baia - is well connected to Pozzuoli public transportation. You can also take a taxi, either from Pozzuoli's Metro station ( it should cost around 25€) or from Naples, where taxis offer a flat rate of 85€ for a round-trip to the archaeological area of Baia and Solfatara with a 3-hour wait.
Cuma - Although local EAV buses are available from Pozzuoli and the nearby Fusaro stop of the Cumana train line, a taxi from Pozzuoli is a more comfortable option.