From your explanation it sounds more like you want to learn about Game Development, not Game Design. If you are interested in Game Development, take Nick's advice. I've done a whole lot of Flash Game development in the past, and all the resources he listed are top notch.
Also, you should definitely check out the following...
mochimedai.com: they provide lots of great resources and tools for Flash game developers, I used to hang out on their forums back in the day when I was creating my first indie Flash game.
BUT, If you want to learn actual Game Design, which is a whole different concept from game development, you should check out this blog
It's by a guy named Ian Schreiber, who co-authors a book called "Challenges for Game Designers". He wrote a blog in which he taught a free game design course over the net, the only requirement is that you had to buy his book, which he uses through the course, which is about 20 bucks on Amazon.
I started the course and then realize that Game Design was not for me, I was far more interested in game development. But if you want to dable into Game Design I definitely recommend it. The course was designed for total beginners, so you need no prior experience in game design to take it.
One of the great things about the course is that you don't do any programing, it's all paper prototypes, which really allows you to focus on the design. Of course this doesn't stop you from taking one of the games you designed during the course and turning into an actually playable prototype/game.