I've seen a few hundred posts asking how to make a game, and no responses showing how to do it for free, so I'll help out anyone who seriously wants to program a game in Actionscript, and not spend $699 on Flash CS3.
1) Download the Flex 3 SDK from Adobe's website. This includes the mxmlc.exe compiler to create SWF files. Cost: $0.00
2) Download the latest version of FlashDevelop. It'll really help with writing actionscript, organizing files, and using mxmlc.exe, the SWF compiler included in the Flex 3 SDK. Cost: $0.00
3) Read up on programming in Actionscript 3.0 (or 2.0 if you want). Senocular has a great intro to using mxmlc.exe and as3 here.
The downside? You have to import all your graphics, or draw things in code.
