How do I download a video from Youtube?

I love watching videos on Youtube, and I've found a few that I'd like to download to my computer.
But I don't know how. My friend at work told me I need to use a website where you type the video url, and then you can download it to your PC.
Can anyone tell me what website is that?

Also, the quality is important, please let me know how to download the videos in the highest quality possible.

There are several websites that allow you to download videos from Youtube.
My favorite is Clipnabber.com.
You can download videos in normal quality or MP4, Youtube's high quality format.
MP4 is a cool format, it looks great and plays nicely in Quicktime.

Also, try Keepvid.com.

These websites work with Youtube and other Video websites too, like Metacafe or Liveleak.