Game design doesn't really exist as a career choice. There are virtually no jobs in the design aspect of gaming that don't also involve some technical aspect. In other words, you won't find a company that will pay you to dream up new games.
There's a simple reason for this. Any gaming company also has programmers, 3D modelers, and animators who also happen to be game designers. Why would they pay for somebody who doesn't also have one of these skills?
If you have good ideas for games, there's only two ways to turn the idea into a game:
Write a game, or write a check. If you can afford to hire a programmer (and maybe a modeler or artist) then congratulations, you're a game designer.
Most of us have to do it the hard way: write some games.
Take a look at Game Programming: the L Line:
(Full disclosure here: I wrote this book, so I do have a vested interest)
I wrote it because I talk to so many people who want to get started in gaming but get bad advice. (I also wrote Flash Game Programming for Dummies, but I think Python is a better place to start)
Learn to program. That's a whole skill-set on its own. The language isn't that critical, but learn how programming works. If you can do it in a language that is easily adopted to gaming (like Python) then all the better. If it's free (Python is) that's even better!
Then learn how game programming differs from more traditional types of software development.
If you want to get into 3D, take a look at Blender. It's a marvelous free 3D modeling program that also has a very powerful gaming and physics engine. Sadly the documentation and books for this program aren't as complete as they could be yet.
Best of luck to you! Please stop by my site and drop me a line if you have more specific questions...