train booking app?

Trenitalia, Italy’s national rail company, has an app: https://www.trenitalia.com/en/purchase/mobile_ticketing.html

Italotreno also has an app

Use the official train sites/apps

We used the trenitalia app a lot a few years ago and found it to be quite helpful for researching and booking both the Regionale and the Frecce trains. The app was pretty intuitive to follow and had the added convenience of not requiring validation of paper tickets for the Regionale trains as is usually the case. With it we were able to finalize a booking as we were literally walking out of our accommodation towards the train station - really convenient.
Your electronic tickets will come to you as an attachment to a confirmatory email you'll receive after you finalize the booking. You'll need to display the PNR's on your phone in order to enter the platforms at the larger stations like Rome & Florence where access is restricted, as well as showing it to the ticket checkers on the trains themselves.

Thank you to all and I appreciate all the details that Robert provides.

I was just trying to add my credit information to my Trenitalia account on the app I downloaded. It sounds like I should be able to do so, but I can't find anything to click on in order to do so. I'd prefer to have the information already added rather than having to add the credit card information each time I buy a ticket. Can anyone help?

Register on the desktop version of trenitalia.com, save that credit card as your favorite method of payment and then use the same account to enter the app.

It's the only way with non EU plastic.

Two days ago, I seem to have successfully bought a Trenitalia ticket complete with PNR and printed it out. I did this on my desktop, comfortably at home. Apparently I did not allow the credit card information to be stored. My credit card bill shows it was purchased through ItaliaRail. I am now trying to make it easy to buy train tickets when I am actually in Italy by using the Trenitalia app as recommended in this forum. I just went on my desktop to see if there was a way to add credit card information as also suggested in an above comment. From what it said on the desktop Trenitalia website, I will have to add the credit card information next time I buy a ticket, and at that point mark to save the credit card information for future use. It doesn't seem like there is any way to do it proactively.

Italiarail is a reseller, NOT the same as Trenitalia
If your cc bill shows purchase from Italiarail then you didn’t purchase on Trenitalia website