I have missed the train. When does the next one leave?
per-SO il TRE-no — past participle perso. PROS-si-mo — stress on first syllable.
Say this at the ticket desk or information point immediately after missing your scheduled train, to find out when the next available service is.
Ho perso il treno (I have missed the train) — perdere il treno is the idiomatic expression. Quando parte il prossimo (when does the next one leave) — prossimo here refers to the next train without repeating the noun.
Il mio biglietto vale ancora per il prossimo treno?
Is my ticket still valid for the next train?
Ticket validity after a missed train depends on the ticket type — ask before boarding
Devo comprare un nuovo biglietto?
Do I need to buy a new ticket?
Some flexible fares allow travel on any same-day train
C'è un treno più tardi stasera?
Is there a later train this evening?
Più tardi (later) — checking if evening services are available
Trenitalia's Base fare (the cheapest) is changeable and refundable — missing a train is not a financial disaster if you bought a Base ticket. Economy fares are non-refundable and non-changeable.