Well, when watching a video on Youtube, there's a box on the right with the URL. Copy and paste the Url when anda add the video to fanpop.
If you're talking about downloading a video from YouTube to your computer...
I use Realplayer. Usually when I watch a video on youtube, there's this pop-up box on the up, right corner of the video stating, "Download this video" It only works with Google for me. I can't get it working with Mozilla Firefox.
Using Realplayer, I can watch the video I downloaded and saved into my laptop from Youtube.