There are many ways to download youtube videos. Some involves browser addons, some are web services, and there are also some software available that help you download youtube videos.
But its also possible to download a youtube video directly from youtube servers using a direct download link.
To download a youtube video in high quality HQ format, copy and paste the following code in the address bar of your browser while on the youtube video page:
To download the youtube video in high definition HD format, copy paste this code in the address bar of your browser while you have the video page open:
Update: Unfortunately, Google has disabled this method of downloading youtube videos and the direct download links no longer work.