If you want to do it the free way you can use Flex SDK [http://www.flashdevelop.org]. You code in ActionScript 3 and flex compiles a .swf that you can play.
You can use a game engine like Mode [http://flixel.org/] from the Flixel help page. A good place to start might be modifying that game (I learned Flixel doing this, but already knew AS3).
Unfortunately there isn't a substitute for learning ActionScript. There are OK tutorials online but I think finding a decent book is a better option because they are more comprehensive, especially if you don't know any programming languages already. Tutorials like this one [http://winterglass.blogspot.com/2010/04/absolute-ultra-beginners-guide-to.html] will get you going but don't really deal with the language, so you're kind of stuck afterwards.
The best place to start is probably by picking up an ActionScript 3 book (a beginner's book or something similar, not a reference book). Go through that and at the same time use what you're learning to modify an open game like Mode. Make sure the first game you make on your own is very simple, and make sure you actually finish it before moving on.