train schedule

Here

https://reiseauskunft.bahn.de/bin/query2.exe/en?protocol=https:&rt=1&

Or directly at the website of the Italian railways: www.trenitalia.com/tcom-en

Thanks. Do trains get sold out? Do we need to purchase tickets ahead of time?

It depends on the route and time of year. You can save a lot by purchasing early though.

Last year when I was traveling in Italy, I found it very useful to have the Trenitalia app on my phone and tablet. It was great for consulting schedules when I was offline. I stumbled on the app in the Google play store. It was called something like tren.it.

There's a schedule update in early June (June 10 or June 12?), so you might be better off waiting awhile to install the app unless you'll be in Italy before the schedule changes. There was also a pdf of the schedule that included route maps available onine last year. I think that may not be ready for download the day the schedule changes; I couldn't find the new one last fall.

The fast trains (Frecce, InterCity) require reservations (extra cost) and can sell out. Perhaps even more important, there are great advance-puchase/non-refundable deals available on those trains when the tickets go on sale. As more tickets are sold, those deals vanish, and you can end up paying far more for your trips.

Some destinations can't be reached by fast trains, and you'll end up traveling on a regionale train. The prices of those are much lower and do not change, there are no seat reservations, and they never stop selling tickets. In theory you can end up standing if you don't step lively when you board the train. I like the regionales because I can keep my plans flexible without spending a fortune on trains. For some shortish routes, there's very little difference in the travel time via regionale vs. a fast train.

If you purchase up to 120 days ahead for the lowest fare, you may not be able to make changes.

pato,

As the others have mentioned, you can check schedules in Italy either on the Trenitalia or Italo Treno websites. Italo only covers a number of high speed routes, but they're a good option in some cases.

Trains rarely sell out, and you can purchase tickets in advance. The main reason to pre-purchase tickets is to save money on the fast trains. There are no discounts for the Regionale trains, so tickets for those are best purchased at local stations (but be sure to validate those prior to boarding the train on the day of travel or you'll risk hefty fines).

Note that the cheapest tickets for the fast trains are non-refundable and non-changeable after purchase, and are specific for only one train, date and departure time, so choose carefully before buying. If you miss the train for any reason, the tickets are worthless and you'll have to buy more at full price. The fast trains have compulsory seat reservations, and those will be included with the tickets.

If you'd like to have more flexibility and have a generous travel budget, you can also buy tickets locally a day or so before travel (even on the day of travel) but you'll be paying Base fare (highest price tier) for tickets on the fast trains. If I'm buying tickets locally, I prefer to buy the day before travel so that I don't have to deal with that when I'm hauling luggage, and when there may be long queues at the ticket office or Kiosks.

The best app to check Trenitalia, Italotreno, Trenord and Circumvesuviana timetables at the same time is Orario Treni by Paolo Conte.
This way you can easily choose the cheapest train and/or fare.
Unlike trenitalia's website, this app will warn you if you're making a search after the next timetable change (June 12 and December 11 in 2016, if I'm not wrong).

As a rule of thumb italian trains do not sell out. Exceptions are Easter monday, long week-ends (i.e. the 25th of April and/or the 1st of May) and the 2 middle weeks of August.