Hello. The two main ways you can download MP3s these days are by download sites - These tend to get shut down quite often depending upon what stuff they have on them so let me know if any links don't work. You can also Try Peer To Peer File Transfers with stuff like Napster, Audiogalaxy etc.
Dj Leekee's Site: www.djleekee.com Check out his Year mix it's cool Just follow the links on the above sites and you will find even more sites with stuff to download.
I use a program called IMESH to download MP3s: www.Imesh.com Soul Seek
It seems to have loads more users than last time I tried it and I'm managing to find quite a bit of stuff. It's better than Kazaa and Imesh etc. coz it doesn't have any annoying adverts.