To get to Takayama from Tokyo, take the Shinkansen (Bullet Train) from Tokyo Station to Nagoya Station. Ask for the superexpress Hikari train; the trip takes about 2 hours. The superexpress Kodama train takes 2 hours, 52 minutes from Tokyo to Nagoya. From Nagoya, take the Takayama line, a 2-hour-and-58 -minute trip to Takayama.
It is a good idea to purchase a Japan Rail pass from any Japan Air Lines office before you go. The pass is valid for unlimited travel on Japan National Railways (JNR) trains, JNR ferryboats, and JNR buses. The costs is from 21,000 yen for one week to 44,000 yen for three weeks, ordinary class, and 30,000 yen for one week and 64,000 yen for three weeks, superior class. There are special rates for children, 6 to 11.
Here is a list of a few books to read before you go, or to take along with you: The New Official Guide to Japan, compiled by Japanese National Tourist Office (this is the "blue guide" to Japan); Fodor's Japan and South Korea, or Fodor's Budget Japan; Japan, A Traveler's Companion, by Lensey Namioka, Vanguard Press Inc.; Eating Cheap in Japan, by Kimiko Nagasawa and Camy Concon, Shufunotomo Col Ltd.; Roberts' Guide to Japanese Museums, by Laurance P. Roberts , Kodansha International Ltd.; Japan Unescorted: A Practical Guide to Discovering Japan on Your Own, a Japan Air Lines guidebook.