Traveling by train is a good way to visit Italy's cities. Driving in Italian cities can be difficult and parking is even worse. Many parts of the city are closed to cars except with a permit and drivers may get fined for going into a zona traffico limitato (ZTL). Most Italian train stations are close to the city center and those that are outside town are connected by bus so traveling to cities by train is fairly easy. If you're traveling on the Eurostar, or fast train, you can sometimes save money by buying your train ticket ahead of time (although train tickets are not usually sold more than 2 months in advance) see When Should I Buy My Italian Train Ticket and Buying Train Tickets Online for more details.
If you're new to riding the rails in Italy, you'll find what you need to know in our article, Italy Train Travel and when you have a train ticket that does not include a seat reservation for a specific train, be sure to validate your ticket before boarding. I've seen passengers on regional trains get fined for not validating their tickets.
Train Travel Videos: Basic Italian for Train Travel | Tips for Using Trains in Italy
It is essential to validate your train ticket before boarding, use the small machines on the platform (usually yellow if memory serves), in smaller stations there may be only one, on the platform closest to the ticket office.