My first experience with video game design comes from just playing THOUSANDS of games.  From there I found this amazing website that allows you to make different types of games, in this case, 3D FPS games.   The site is called Storm the Castle.  There are TONS of different activities on this site, but the focus of this page will be video game design.

http://www.make-video-games.com/video-game-design/index.htm