Now you've got the flex3 SDK you can create AS3 classes using a text editor and use them to build flash movies using the command line tools that come with the SDK.......If like me you're too lazy to manually build your swfs there are a couple of very good free IDE's which can be used with the Flex3 SDK. Flashdevelop (www.flashdevelop.org) or eclipse (www.eclipse.org) are the best. Personally I use Flashdevelop (only available for windows at the moment!!).
Not sure on what to do with eclipse as I've never used it, but with flashdevelop it's just a case of downloading and installing the latest version. When you attempt to build your first AS3 project, the IDE will ask you for the path to the flex 3 SDK. All you do is navigate to the folder containing the flex3 SDK and hit OK. And that's it. You can now compile and build AS3 projects.

Flashdevelop supports using mxml/AS3 or pure AS3 to create flash content you can even create apps for adobes AIR runtime environment as well as using Haxe there are even options to create AS2 based projects.

cheers for now,
Jas.

p.s. there are tons of tuts and examples on the flashdevelop forums!