When you purchase a train ticket in an unfamiliar area, pay attention to the policies, both those presented during the purchase process, and any that may be written on the back of the ticket. Validation is a common requirement in Europe and, as with Trenitalia, it is typically accomplished by inserting your ticket into a validation machine on the platform. There are other rules you may not expect as well. For instance, if you’re traveling with a Eurail pass (multiple city travel on one ticket), even though it is stamped when you book it, it has to be stamped again by an official at the train station before your first journey, where you must give your passport number and signature.
There are signs in most train stations advising passengers to validate their tickets (albeit in Italian, but it is Italy after all). While not all tickets need to be validated, many do, and the rule is written on the ticket, which means the company has the right to enforce the policy. I understand if you ride Amtrak, or commuter rail in the New York City area, the notion of validation may seem odd since the conductors punch every ticket, but trains in Italy are often big enough, and conductors few enough, that a conductor may not reach you before the end of your journey. You could easily leave the train with a ticket that could be used again.
If policies are not written in English and you don’t speak the language, take the time to decipher the information. You could use a translation app on your phone, such as Google Translate, iTranslate, or Waygo, which works with Japanese, Korean, or Chinese characters. Or, better yet, you could find someone to help you—think of it as an opportunity to strike up a conversation with a local (You never know). In addition to getting your ticket properly punched, you might learn about a great neighborhood or restaurant that has never made its way into a guidebook. And, since the conductor won’t demand extra funds, you’ll have more money to spend when you get there.