This isn't exactly the easiest thing to accomplish if you're not using Firefox. So, get Firefox. Download the Download Helper add-on. That's it. Once you have this installed, you'll have an icon on your toolbar.

Navigate to a web page that has YouTube videos on it, then click the drop-down and you'll see a list of the YouTube vids on that page and you can download them to your computer.

Now that you've got the FLV file saved to your computer, you'll need something to play it. It's doesn't get any better than VLC. Download, install and you're on your way.

If you're using IE, then you'll need a separate program to download the files. Look here for a good list to get started. You can also try SaveYouTube.com, but I have found that it doesn't work all the time.

I finally got smart and decided to post some reference material for myself, seeing as tagging works like a charm in the ol' tag cloud. So off we go...

1. Prepare the AVI file. And by prepare, I mean make it available. And by make it available, I mean don't have it deleted. And by don't have it deleted, I mean have it edited to your satisfaction.
2. Login to your YouTube account. I use my Google account, so Blogger & YouTube are all in sync.
3. Upload the video. You'll have to make it public in order to share it, but I disable comments, ratings and responses since I don't really care about that. Keep in mind that it will be public.
4. Wait. AVI file's aren't smallish, and chances are unless you're uploading this from work, you'll have a poky 384kbps or less upload speed. So grab a spot of tea.
5. Once the upload is finished, YouTube presents you with a nice bit of HTML that you can copy and paste into your post! Voila!
6. I should note that it does take a bit for YouTube to process the video, so if you immediately post with your embedded object, you won't be able to access the movie. Instead of seeing the preview of the movie, you'll see a generic camera image, and after pressing play you'll get a message indicating that the video is no longer available. Just sit tight. Depending on the size of the movie, it may take anywhere from a few minutes to an hour to prepare. In my recent exercise, I noticed that a 33MB file took around 5 minutes to process.