If you're thinking about travelling around Italy by train, you should always check the railways website http://www.trenitalia.com for special offers. If you register and book online you can get some fantastic bargains.
Currently there is a 'Happy Train' offer where you can buy 'last minute' tickets (travel within the next seven days) from €10. There are also €15 tickets for a range of trains including Intercity, Intercity Plus and overnight services. Deals on the fast Eurostar trains start at €29. This could save some money on longer journeys (always check the standard price too), and these special prices often give you the option of travelling in first-class for the same price.
You can check availability online - when you are booking your journey, select the appropriate tariff. Sometimes the Italian version of the site has more up-to-date information and bargains (if necessary, sit down with a dictionary; the savings are worth it).
After one attempt to buy tickets in person in Rome (witness to a disagreement which culminated in the ticket clerk calling her customer an 'ignorant pig' and then slamming her kiosk shut in front of a line of customers) I have made all my bookings online or at the machines in stations. The system is amazingly efficient, and you can even travel without a ticket on many services, as long as you have your booking reference number and details. I've travelled the length of Italy for bargain prices which have sickened my Italian travelling companions. I even have a reward card.
Read more about the different types of train in Italy. My long account of an even longer journey from Rome down to Sicily can be read in my blog: Slow train to Sicily. Yes, Sicily is an island, but you can get a train all the way there; it's taken apart, rolled onto a boat, then rolled off again at the other end of the crossing.