First off, what is a Japan Rail Pass. The Japan Rail Pass is a pass issued by Japan Railways (JR) with which you can travel (almost) unlimited on trains of JR, hence it cannot be used on trains and subways from other companies like Toei, Tokyo Metro, Keisei, Tobu, etc., only JR lines.
There are basically 2 types of passes: Ordinary and Green. Different prices for adults and children and the pass can be purchased for 1, 2 or 3 weeks.
The difference between Ordinary and Green, is that with Green you can reserve seats on Green cars, meaning first class cars. With an Ordinary pass you can only reserve seats on second class and you cannot ride on the Nozomi trains of the Tokaido&Sanyo Shinkansen.

IMPORTANT NOTE
A Japan Rail Pass CANNOT be purchased in Japan! First you have to purchase an exchange order in your home country. This exchange order can then be exchanged for a Japan Rail Pass in a major JR Station or at the airport.
Look on the Japan Rail Pass website for addresses where to buy them in your country: http://www.japanrailpass.net/eng/en005.html.

For more information see on the Japan Rail Pass website: www.japanrailpass.net

Once you have exchange your voucher for your actual Japan Rail Pass, it's time to use it. When you ride on JR trains, go to the ticket gate and look for an little office on the side of the ticket gates. Show your pass to the official present and he will open the gate for you. They are usually very friendly and some hardly look at the pass but some check it quickly.

Reserving tickets on the Shinkansen.
to come

Here are some pictures of a Japan Rail Pass (pictures may differ from other types of pass). The pictures are not that good, I took them quickly with my camera, will scan them later.