Well, there are a couple things you can go to get your game made:
1. Contact independent game designers- you aren't going to be able to get through to anyone at a large company like EA; however, there are a bunch of small independent companies always looking for the next big sleeper hit.
2. If you don't mind using the xbox 360, get yourself a copy of XNA. It is microsoft's gaming dev kit, and it is supposed to be user friendly enough that ANYONE can create games with the software (and unlike most development kits, it only cost $99, and is aimed at independent designers to create games for xbox live).
3. Because you would be programing for either Wiiware or Xbox Live Arcade (games that sell on store shelves are incredibly expensive and difficult to make), find a local programmer that would be willing to go into business with you (check out your local colleges, there is always someone looking to break into the industry).
There is one thing you want to note:
Nintendo is notoriously hard to work with (although easy to program for), there is a reason most 3rd party software sucks on Nintendo consoles.
Good luck!
Update:
I just realized I didn't really answer your question. To contact an independent studio, first find a game that is similar to your own (be it geometry wars, world of goo, etc...), and with independent companies it is simply a matter of calling those companies and trying to set up an appointment with a project manager. When you do call, you are going to want to speak to the manager, not the designers.