First you will need VLC Player (Free from HERE) Download and install.
Open VLC Media Player Go to the Youtube video you wish to save, right click and copy the link In VLC Media Player, click on "Media" at the top left of the screen. Paste the link in the "Open Network Steam". Click play, then right click and record.
It will automatically save the recorded clip to you computer. Do not stop the video, you must let it run all the way through.
This is just for reference only so you can save the video to your computer without having to use the internet every time you wish to view it. The video itself belongs to the original uploader/authour and this must be acknowledged.