How to download from youtube and vimeo

[joe at actionline.com]

What is the procedure for downloading and saving to disk videos on
youtube and vimeo?

In particular, I found this really impressive video that I would
like to save and try editing with open shot:

http://vimeo.com/18198228

On the page, there is a link labeled: "Download" and when I click on
that link, four download options are listed (various resolutions)
but when I click on any of those links, the video plays, but I
cannot find that the video is downloaded and saved
anyplace on my system.  What am I doing wrong?