That's reasonably easy, actually. First you need a program to record the sound as it is playing. I use Sound Forge 9 from Sony, but there are a bunch of free or at least cheaper programs available. I like Sound Forge because I have used it for years both at work and at home. It does what I want it to with a minimum of fuss and is for the most part intuitive to use. I paid about $80 for my copy at Target and consider it well worth the money.

Audacity, a free program which is liked by many is available at download.com. http://www.download.com/Audacity/3000-2170_4-10058117.html?tag=3150&cdlPid=10606824

Start the recorder then start the youtube, preferably from a downloaded file, especially if you have buffering issues.

You may have to fiddle with your sound settings in order to get the recording program to recognize the sound playing through your speakers. My current computer is the first one that I had to make those changes. Earlier simpler ones were properly set in the first place.

If this doesn't get you started, we'll talk again.