[1]Copy the URL of the video you want to download.
[2]Paste the url on
http://youtubeloader.com/
[3]Right click on download link and click save target as.
[4]Open in any media player that supports flv video files. I recommend VLC for any kind of music or video.
VLC media player - Overview
For those with greasemonkey there is also this userscript which adds a download link on youtube pages
Download ANY Video from YouTube – Userscripts.org
Optional: You may convert the flv file to another format but that's another guide all together. No converter comes to mind at the moment. Will update when I think of a good free one.