So, I've been asked a few times now how that works, so I thought I'd spare myself some typing and just tell people to check here <_<
You only need 2 things.
First: A Firefox plugin to download the videos. Like
this one.If you don't use Firefox, you fail 8D
Second: A converter. I suggest
Super, cause it's free and can convert many different formats just through drag & drop~
Put the file in there, choose mp3 as format, click encode and you're done.
Hope this helps.
Edit: Plugin that works with FF 3.0
here.