Mary,
I'd also suggest buying P-P tickets when you arrive in Italy. With only 3 trips, a Rail Pass would not be the most cost effective option (especially as you'd have to pay separately for reservation fees which are compulsory on the "premium" trains such as the EuroStar Italia or Cisalpino).
I normally research which trains I'll be taking using the bahn.de website (it's incredibly helpful!). If you have a fairly good idea on which trains you want to use, you could perhaps purchase the tickets for all journeys when you reach Milano Centrale. These would include reservation fees, if applicable. Note that you'll normally have to validate your ticket in the yellow machine prior to boarding the train.
You'll need to check the large sign board to verify which Track No. (Binario) your train is departing from. If you have a reserved seat, the ticket will specify the Train No. (Treno), the Car No. (Carozza), the Seat No. (Posti) and whether this is Corridor (Dorridoio) or Window (Finestrino).
As this is your first trip to Europe, I'd highly recommend reading at least the "Rail Skills" chapter in Europe Through The Back Door, as it provides a lot of information on how the rail systems work. The information is also available on this website in the "Rail" section, in the PDF Rail Guide.
When you check your rail journeys, try to choose routes with minimal changes. On the trip to the Cinque Terre, you'll most likely have to change trains in La Spezia and use the small local train to whichever of the five villages you're staying in. The local trains have frequent departures (times are listed in the Italy book).
I normally pack the Guidebook along when I'm in that area, as the simple Maps make it easy to get oriented in each new town, and get to the Hotel.
Be sure to pack light (important if there will be train changes and you have to use the tunnel to get to the next track) and wear your Money Belt.
Happy travels!