Below is the typical "flight board" or "departure board" that you'll see in Italian Train Stations. This one was in Venice. It's interactive; follow the instructions to learn what each component of the board represents.
Italian Trains - More Information
Tickets are usually bought in the station. You can check routes on Trenitalia. Trenitalia also has a good explanation of all their National Trains.
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or to purchase train tickets in advance, Click here for Rail Europe.