The Italian train system is genuinely excellent. High-speed trains connect every major city. They are affordable, comfortable, and mostly on time. This is not the problem.
The problem is buying the ticket.
The two systems you need to know
Trenitalia is the state railway. Italo is the private competitor on high-speed routes. They do not share tickets, apps, or anything else. You need to check both for the best price.
How to actually buy tickets
Go to trenitalia.com directly. The app works but the website is more reliable for first-time purchases. Book early for high-speed trains — the cheapest fares (Base tickets) sell out. Regional trains have no reservation required, just board and validate.
The validation ritual
On regional trains, you must validate (stamp) your ticket before boarding. There are small yellow machines on the platform. If you forget, you can be fined even if you have a valid ticket. The inspector has heard every excuse. He does not care.