One of the cool new features of Adobe Flash 8 Professional is the Import Video Wizard. Flash converts your original video files (.avi, .mov, .mpeg) to a flash video file (.flv) that is compressed, progressively downloaded, cached, and then played from your flash movie.
With the release of Flash CS4, Adobe gave us a new flash encoder (Abobe Media Encoder). Check out this instructional video to see the differences.
With the release of Flash CS3, video encoding has changed a little to make it even easier. Check out this instructional video to see the differences.
The Import Video Wizard steps through the process of selecting your video file, specifying the compression, and choosing which playback control to use. It takes only minutes with no ActionScript code to write.
To publish your flash video, you include your video file (.flv), movie file (.swf) and the FLVPlayback component file (.swf) as well. Almost any web hosting plan will play these flash video files, so there is no extra cost (unlike streaming video). Adobe has a great article on Flash video, as well as this article (.pdf) written by Sas Jacobs explains the whole process step-by-step. For a little more technical explanation try this article too by Tom Green on Digital Web Magazine.