The main classes are JGEngine (the whole game) and JGObject (a sprite object). Sublass these to write your own game. The methods you are supposed to use are the public methods in these classes (make sure to generate this javadoc with -public). It's handy to have your JGObject classes as inner classes of your JGengine. JGTimer is used for creating timers in your games. ImageUtil contains some stand-alone image manipulation methods.
JGame should also come with a user manual (the file MANUAL). It is distributed under the revised BSD license (see the file LICENSE). More information can be found on the website, http://www.13thmonkey.org/~boris/jgame/