I get asked this question quite a bit as YouTube is increasingly blocked at more and more schools and teachers want to get content from home and bring it to school to share in their classrooms.
There are literally hundreds of ways to do this which I go into great detail in The ultimate guide to YouTube for educators but the simplest way by far is through Realplayer Basic.
RealPlayer Basic can be freely downloaded here and takes a couple of minutes to install. Once installed the next time a YouTube or any other form of web based loads on your desktop a little icon will ask you if you wish to download this file. This will be instantly saved to your designated video folder and it will then offer you to convert it into a variety of formats once complete.
I have included an instructional video below for visual learners. This was obviously put together by a teenage boy as you will find out. Good luck