The main station in Naples (Stazione Centrale, at Piazza Garibaldi) is also the main interchange node for public transport both east and west of Naples. A branch of the aptly named Circumvesuviana railway serves the main archaeological sites at the foot of Vesuvius. Trains leave from the Corso Garibaldi station in Naples, stop at the main terminal at Piazza Garibaldi 10 blocks away to link up with the Naples metropolitana, and then head southeast for Sorrento (about two trains per hour; EUR 1.70 to Ercolano and Torre Annunziata, and EUR 2.30 to Pompei Scavi-Villa Dei Misteri). Confusingly, the station called "Pompei," which is the stop for the modern city, lies on a different line, which will leave you not at the main entrance to the archaeological site but just behind the cathedral, close to the amphitheater.
For the Phlegrean Fields to the west of Naples, take the Cumana line run by SEPSA, with trains every 15-20 minutes, from the terminus at Piazza Montesanto near Montesanto Metropolitana station. Alternatively, take the Metropolitana all the way to Pozzuoli from one of the railway stations in Naples, either Piazza Garibaldi or the more welcoming station of Mergellina, with one departure every 10-15 minutes. This will drop you near the amphitheater and the Solfatara crater.
When not affected by wildcat strikes or landslides, the railway network on either side of Naples is cheap and reliable, though with the many stops along the way you're unlikely to experience nerve-tingling velocity. As in many other mass transit systems, pickpockets operate, especially around Piazza Garibaldi, so if boarding a train here, stash your valuables in an inside pocket. If buying a ticket, have some coins or small-denomination notes ready.
Circumvesuviana railway (081/7722444. www.vesuviana.it). Mergellina (081/5543188). SEPSA (081/5513328. www.sepsa.it).