A lot of these tracks are released on people's blogs so the first thing I do when I want to find a track is type:
(Song name & Artist) + MP3
in google. If I can't find it in the first couple of hits I try:
?intitle:index.of? mp3 (song name & artist)
Sometimes you'll get really lucky and find somebody has uploaded every song they've ever had onto some random ass webpage. I found a site with 10 000+ miscellaneous songs on it using this.
If I can't find it I finally use frostwire. It's basically a limewire knockoff but it's open source and removes most of the limitations that free limewire has. Some people will recommend bearshare or others but as I already have uTorrent I don't need another bittorrent client too. I've tried half a dozen different gnutella network clients but I always end up coming back to frostwire.
Sometimes songs you'll find on youtube are impossible to find. I then have to resort to
it will rip an MP3 from any youtube video so if you absolutely must have a song and don't mind a slight drop in quality this is the only choice you have.
Hope that helps.