Wow.. there are about a million places to download music for free. It's hard for me to believe that people still pay so much for single songs and ringtones, unless there is some ethical reason behind that choice. It would help if you could tell us what type of music you are interested in, and from there I'm sure I could recommend you a few places to go. You could start off by going to my music blog http://digitalmeltd0wn.blogspot.com Chances are you may be unfamiliar with much of the music posted there, but to me and many others it is considered good if not great music. I would also suggest checking out the skafunkrastapunk forum. Almost anything you can think of is posted there http://skafunkrastapunk.com/forum I know of dozens of other ways to find just about anything you're looking for, but for someone who is new to downloading music I think music blogs and forums are a good starting point.
Here's a few more useful links for you. Totally Fuzzy - This is what they call a music blog aggregator. It's a fantastic resource http://tofuhaus.antville.org/ The Authentic MEGA SUPER MAMMOTH mp3 Blog List - The title says it all http://gravybread.wordpress.com/mega-mp3-site-list/