Trenitalia is the trading name of the State-owned Ferrovie dello Stato (National Railways). It has a comprehensive network of lines serving almost all towns of any importance, and many minor places. It operates a number of different kinds of trains:
Frecciargento and Frecciarosso trains are very fast trains that provide the main service between major cities, running on dedicated high-speed tracks.
Frecciabianca trains are older but modenised fast trains, generally providing services to less important places, and operating on traditional train lines.
InterCity trains use older rolling stock and provide services between major cities, but operating on the traditional train lines and making more stops than the faster trains.
Seat reservations are required on all the above trains, and are included in the ticket price. Tickets usually go on sale four months before travel. The really cheap tickets often sell out quickly, so buy early for the best prices.
Infants travel free up to and including their fourth birthday, but are not entitled to a seat. Children over this age and up to and including their 15th birthday can travel at a 50% discount. This discount is applied to the full fare, so it may cost less to buy a cheap adult ticket.
Regionale and Regionale veloce trains are slow trains, often using old rolling stock, that provide services to smaller places. They make frequent stops. These trains have no seat reservations (so tickets cannot sell out) and there are no discounts, apart from half-price fares for children up to and including their 12th birthday. Tickets bought online have more restrictions than those bought in Italy, so buy Regionale paper tickets at a train station in Italy.
Trenitalia has a timetable change on the first weekends in June and December. This seems to require protracted nagotiation with national and regional government about the level of service and the amount of subsidy. The new times may not be available until mid-May or mid-November. The times usually do not change much on main routes.
Italo is a private enterprise competitor to Trenitalia, and started its services in 2012. It has a limited network, serving only a few major cities.
At present, Italo operates only one kind of train providing very fast services that are comparable with Trenitalia's Frecciargento and Frecciarosso services.
As with Trenitalia, it is best to buy early for the best prices. Read the terms and conditions on the discounted fares. The time when tickets are released seems to vary somewhat.
Italo operates over the same tracks as Trenitalia, so its publication of timetables may be affected by Trenitalia's delays in setting its timetable in June and December.