First, to design a game, you need the design. Good games always have a solid design under them. Known as a design document, this defines what your game is going to be and all people working on the project adhere to it. The design document can (and should) change, as testers give their input, but the main concept and idea of the game should remain the same.
After you have the design down, you have to start programming the game. C++ is the language of choice in programming games (IMHO anyways). First you should pick up a C++ book at your local bookstore. Not just a beginner 'tutorial' or anything ('C++ For Dummies', 'Learning C++ in 24 Hours', that kind of stuff), but also a complete reference guide ('C++: How To Program'), because you'll need it in a few years. 3-4 years at the minimum is required (IMHO again) to program a game with DirectX or anything else COM-based. 2 years for OGL, because the API is much easier to understand.
I would personally suggest that you get a book on DOS game programming. Although they may be 'old' or 'outdated', DOS programming enables you to learn many things you wouldn't be able to learn as easily in the Windows world (i.e. plotting pixels, simple OO based programming, palettes, animation, system-level stuff, sprite drawing, ... ...). I'm not saying you can't, but why bother with all that HWND and WNDCLASSEX stuff when you can just have an int main() and start making simple games??? For this, get a book like the 'Black Art of 3D Game Programming' (LaMothe).
Once you feel you're ready, I would suggest starting with OpenGL. Create simple windows and make little OGL demos with, like, spinning cubes or something. Then, get a real book on game programming, because you'll need to learn the structure so your code doesn't become spaghetti-code. One great book here (DirectX) is 'Programming Role Playing Games with DirectX' (Jim Adams). It may be with DirectX, but many of the concepts can be ported to any API. One of the best tutorial/reference books out there.
And that's about it. END OF LONG RANT.