To get from Roma Termini, Rome's main train station, to Napoli Centrale, Naples' main train station, there are several train options. Trains run directly between the two stations so most trains don't require a change at another stop. Trains run from early morning (currently 4:52) until late at night (currently 22:13). Here are options, starting from the least expensive:
• Rapido (R) and Regionale - the slowest and least expensive trains take nearly three hours. Rapido trains usually have only second class with no seat reservations.
• IC and ICplus - Intercity and Intercity Plus trains take just over two hours. They have first and second class compartments and seat resrvations can be made (mandatory on ICplus). Cost is almost double the cheapest rapido fare but since trains can be crowded, having a seat reservation is a good idea.
• ESA or ESfast - Eurostar trains take less than two hours, have first and second class compartments, and seat reservations are mandatory. These are about triple the lowest rapido fares but much faster. Note: there are some Eurostar trains that go to other stations in Naples (not Centrale)