Booking train tickets in Italy is a very simple process today. Of course you can get to the train station, stand in line and buy the ticket at the counter. On the other hand, you can easily keep up to date with all the train times and ticket prices and also reserve a seat for yourself in advance (sometimes even at a more discounted price than purchasing at the station itself) – all this can easily be done online.
The most common train companies in Italy are Trenitalia and Italo. Each of them has a website that is convenient to browse both from the computer and from the cell phone. Choose the English language.
A site that brings together all travel options in Europe (including buses)
For the diligent among you, you should compare prices between the different sites. Sometimes, though not always, there are differences.