Thanks to all the forum posts and other useful info on this website, we were able to meander through Italy on trains for about 75% of our recent trip. Here are a few "lessons learned" that might be useful for others:
The self-service ticket machines in train stations are great and you can select your language on the first screen. HOWEVER, like computers everywhere, sometimes they are "down". We ran into a few places where there were two or three machines, but only one was working, and the ticket window was closed. This can be a problem for those who expect to walk into a station and get their ticket just a few moments before the train departs. The line at the single working machine went out the door, and many of the people trying to buy tickets were new to the many-step process and this backed up the line considerably. So get to the station early to buy your ticket, especially if in a smaller town. We also ran into the situation where all of the machines were "down" and there was a very long line at the single open ticket window (in Lucca).
We ran into one train station where the window was closed and the self-service ticket machine would only take credit cards (with PIN) or Euro coins, not bills. We were using our card, but several travelers had to run into nearby shops to get change (which some shopkeepers are reluctant to do without a purchase).
Depending on your particular route, you might end up on a mix of Regional trains and faster trains. The self-service machines (and the website) will present all of your itinerary options after you select your start and end points, desired day (and time range) of travel, displaying the price and travel times for each option. The screen will show any connections or changes you might have to make, etc. The non-regional train tickets will include the printed date, time and other particulars such as car # and seat # (since you are reserving a seat). HOWEVER, if there is a regional train in the selected itinerary it will just print a "generic" ticket from point A to point B good for 60 days. The information from your selected itinerary is not printed anywhere. MY ADVICE: jot down the itinerary shown on the computer screen before you buy so you will know the correct regional train departure time to make your connection.
Other posts in this forum mention getting discounts by buying tickets in advance on the Trenitalia website, but we were being a little more flexible in our travel plans, so I just plotted out our plans about two weeks or so in advance and went to the train station in one of the larger towns (with lots of machines) and just purchased several days worth of train travel at once. (Jotting down all of the selected itineraries as I went (burnt once on that!). You can get tickets for anywhere - you don't have to buy them in the specific station from which you are going to depart.
Just a reminder - don't forget to "validate" any regional train tickets before getting on the train!