You will need a Flash Video Downloader (there are several free ones to download). One would be YTD (YouTube Downloader) Video Downloader:
http://www.youtubedownloadersite.com/; the Basic is free with no converter. That means you'll need another software to convert the .flv files into .avi files. Translation: you'll be able to view the .flv videos on your computer, but not on anyone else's (unless they have a converter installed, too). If you want to burn the videos to disk to share with others or view them on TV, you'll have to have the converter. A good one (also free) is Format Factory:
Format Factory Home Page - Free media file format converter.
One caveat: even when you convert the .flv videos to .avi, there is no guarantee that they will work on everyone's DVD players, as there are so many different formats. They will work on your computer, though. (I don't know about MACS).
Now, it is even easier if you're using Firefox. There are a couple of addons that will do the job nicely, and with less hassle (for the downloading, only). One is: Flash Video Downloader YouTube Downloader 3.6.8 and the other is: FVD Suite Addon 14.0.3
I know this sounds intimidating, but really it isn't. And it really helps to have those videos available to use anytime.