The quickest way to find free MP3 downloads at GarageBand (not every artist features this service) is to navigate to GarageBand Genres. This is where you'll be able to find music that "sounds like" something you're already familiar with, such as the Dave Matthews Band, or Sarah McLachlan. Click on any artist, and then when you get to that particular artist's page, you will see a button that says "download MP3." This will give you the option to just play it in your chosen media player, or download that song in an MP3 format, and from there that MP3 will be placed on your computer wherever you choose to put it.
I've found that GarageBand is a wonderful place to find independent artists, and who could pass up free music?