Step 1 is simple. Use any recording device - a Flip Video Camera, an iPhone 3GS, a digital camcorder - to record yourself teaching. Make sure your video recorder can record videos long enough. If you have a choice between an HD video recorder and a plain video record, go with the plain one. This will make the editing process easier.
This step will vary depending on your camera. Some, like the Flip, will plug straight into your computer and allow you to download the file to the desktop. (Please be aware that the default file type for Flip is MP4, which Windows MovieMaker does not recognize.) Others will require you to "import" the video using software like Windows Movie Maker or iMovie. If you're not sure, check the instructions that came with your video recorder, or ask at the Digital Media Studio.
Both of these programs are free for Windows or Macintosh, respectively. Use these programs to clip your video down to the important parts, and add titles explaining what viewers are about to see.
Once you're finished editing the video and you like how it looks, export (or Share, in iMovie) the video to a file that can be uploaded to YouTube, e-mailed, or put into MavSpace.