To book accommodations, contact Norwegian State Railways at 011 (+47) 815 00 888 or visit their Web site (see Resources, below). Enter Oslo as your departure city and Lillehammer as your destination city. You will then need to select your travel preferences (date, time, number and type of tickets, et cetera).
Choose which class of ticket you prefer (economy or first-class) if the trip you wish to book offers a choice of seats. Not all of the trains will offer first-class accommodations--it depends on the train's final destination beyond Lillehammer. The economy seats are quite comfortable, although they have a bit less leg room (and smaller luggage stories areas) than do the first-class ones.
Supply your name, address and phone number, then select which credit card you'd like to use (the choices are Mastercard, Visa, Diners Club and American Express). The price for your ticket(s) will be shown in Norwegian Kroner (NOK), and you may wish to convert this to your local currency so you'll know what you're paying before your credit card bill arrives.
Pick up your ticket at the train station in Oslo. Be sure to arrive ahead of your scheduled departure time so you will have time to get your ticket and be in line early for the train, as the earlier you board the less your chances of getting poked in the leg with a ski pole.