Plan your trip to Oslo, the departure station for most intercontinental travel, if you are traveling from a different Norwegian city. Most cities can be reached by train (a rail map for Norway can show you possible routes), although if you are up in the far north you may need to take a bus or even a boat.
To book accommodations, contact Eurail at 1-866-638-7245 or visit their Web site (see Resources, below).
Use the 'Timetable and Route Planner' calendar to select your preferred travel date, then type Oslo and Helsinki (or Rovaniemi) into the 'From' and 'To' fields. When prompted on the next page, select OSLO (N) and HELSINKI (F) from the drop-down menus (choosing Rovaneimi will not require you to make a further selection as there is only one station in that city).
Reserve your seat (and sleeper car, should you desire one) by clicking on the 'Easy booking here' link at the top of the page. This will take you to an order form.
Fill out the form, specifying travel dates and preferred time of day, then continue to personal and payment information.
Book your ticket from Norway within 60 days of your trip at any train station. Book any needed tickets to Oslo at this time as well.