We packed up after one night in Rome and walked to the train station. Roma Termini was a 10 minute walk from our hotel. We had bought our train tickets online before traveling to Italy. The one way ticket was 39 euro and the ride would take 90 minutes.
If you don't buy your tickets ahead of time, you can always buy tickets for same day travel at these machines. You'll either need coins or a credit card with a PIN number. The machines have an option to change the language to English. Just type in destination and time tables will show. Select the time you want to depart and continue to the payment.
Once you have a ticket, look on the big departure boards to see which platform your train will depart from. Note: sometimes your destination will not be the last on that specific train line & thus not listed. It's easiest to look for the departure time and double check that it's really your train. The platform will show on the last column.
This is really really really important. Before boarding the train, be sure to get your ticket verified in the machines near the platform. The fines for not verifying your ticket are pretty steep in Italy. The trains were fast and convenient. We were in Florence before we knew it....well after a nap of course.