I'd definitely recommend getting a Japan Rail (JR) pass before you arrive in Japan as Shinkansen (bullet train) trips are very expensive if purchased in Japan. When I spent time in Tokyo I just purchased tickets between the main stations and these were fairly inexpensive - generally between 150-300 yen one way. about 10 years ago
If you will be covering a lot of ground in your travels, the railpass is a great idea. If you will be basing yourself in one city and staying local, however, you may not get your moneysworth from the pass. When you have decided your itinerary, have a look at the Hyperdia site and calculate your fares to see if it'll be worth it or not to get the pass. about 10 years ago
The best way to work out costs for trips around Japan is by using: http://www.hyperdia.com/
The website is an excellent source for finding out train times and costs. There's a link for English in the top left of the homepage.
And yeah, the JR Railpass is amazing value if you plan on travelling all over the country. There are also railpasses for different regions, but at ¥28,000 the railpass beats the ¥100,000 I'll be forking out next week to travel around with my parents (I'm going to Hiroshima, Osaka, Kyoto, Tokyo and Yokohama and can't get a railpass on my working visa). Make sure you buy a railpass *before* you come to Japan as tourists can't get there here. PM me if you need more info. about 10 years ago