Copy/paste youtube link on http://savetube.com/
Click "Go"
Click "Download"
Choose where on your PC you want to save the file to
The file gets saved as a .flv file, so you need a converter to convert it to an mp3. I use a program called Super (google "download Super" & follow a link, i.e. 2nd link to get to: http://www.afterdawn.com/software/vi...ders/super.cfm)
Then you can just drag & drop any file into Super, select the "Output Container" as "mp3 (Audio Only), & click "Encode (Active Files)" it'll convert (average song should only take a minute or so).

*Edited b/c direct dl link wasn't working.