There are two methods for this:

Method 1

1. First of all, look on YouTube the song you want to download, and copy the link in the link bar

2. Next, go to this site : YouTube to MP3 Converter - Video2mp3

3. Now, copy the link from YouTube to the "VideoURL" bar in the site, hit High Quality and click convert

4. After you wait a couple of seconds (or minutes depending on your connection), you click "download as mp3" or just wait 20 seconds.

Method 2

1. First you download this program "Any DVD Converter Professional", and then click on the YouTube icon, then paste the link from the video and hit OK (make sure the profile is selected as mp3)

2. Now click on the Convert icon and wait.

3. The default directory for stored downloads is C:\My Documents\Any DVD Converter Professional\MP3 (for downloads as mp3's)