laura, as the previous Post indicated, there are no "formalities" on the Circuvesuviana trains. Some of these trains are emblazoned with graffiti and a bit "rough looking", but just find whatever seating is available.
You also asked about "Italian trains" and the situation is a bit different there. Especially on the high speed ICE trains, reservations are often compulsory. DON'T be caught without a reservation, or you'll be nicked with a fine on the spot!
You might find it very helpful to read the "Rail Skills" section of Europe Through The Back Door or the rail info section on this website.
AFAIK the Circumvesuviana web site does not have an English section. Is there a particular date and time that you're looking for? You might also check the bahn.de web site, as they may have schedules listed for the Circumvesuviana trains. As I recall, there's also information in Rick's Italy book on those. As they are commuter trains, they run fairly frequently.
The Circumvesuviana trains have a bit of a "reputation", so be sure to wear a Money Belt and keep a close watch on your luggage.
Hope this helps?
Happy travels!