You will certainly notice an element whose size is over 0.5MB (most of the time, over 5MB). Double-click on it (even if it is still loading), and Safari will download it. When the download is over, navigate to the file in the Finder (which will probably be called get_video) and add the extension .flv to its name. Now you can play it with VLC or with QuickTime (only if you have Perian installed).
[robg adds: We've covered the use of the Activity window before, but with the popularity of YouTube, I felt it was worth pointing out this one specialized use.]
[For more on this topic, see Christopher Breen's Macworld story, How to download YouTube videos using Safari or Firefox.]

