There are quiet a few ways to get music off the Internet. I won't go into the legalities of all of them. Obviously, if you are getting someones copyrighted material without paying, then that's probably not legal.
There are services that you can use to get music that WILL pay the artists who created the songs. The most popular are probably...
Apple iTunes -> http://www.itunes.com
Napster -> http://www.napster.com
and even WalMart -> http://www.walmart.com/swap/SwapEntry.do?dslURL=/swap/LoadMain.do%3FmainCategoryId%3D2500
All of these services will sell you songs between .85 and $1.00 per song or so.
There are quite a few services advertised on Clickbank that make the promise that for a one time membership fee, you can download an unlimited number of songs. Here are those services. I cannot attest to how well they work, so research them by visiting them...
Unlimited Download Center -> http://watersaffl.udc01.hop.clickbank.net?tid=YAHOOANS
Movie Downloads.com -> http://watersaffl.movies01.hop.clickbank.net?tid=YAHOOANS
Unlimited MP3 Music -> http://watersaffl.gamecity.hop.clickbank.net?tid=YAHOOANS
Hot MP3 Downloads -> http://watersaffl.mp3hot.hop.clickbank.net?tid=YAHOOANS
I have had good luck finding music on BitTorrent sites. BitTorrent is an Internet protocol for moving very large files. It's not the same as P2P (limewire and such), but it relies on other users in the BitTorrent community leaving their music files available. I have often been frustrated by downloading a song or album only to find that after it downloads 95%, it stops because not enough BitTorrent seeders have kept the files available. The upside to BitTorrents are that they download extremely fast!
You'll need a BitTorrent client to download torrents. I use Azureus. It's a free and very nice client application that you can get here...
http://azureus.sourceforge.net/
You'll also need a few BitTorrent tracker sites. Here are a few to get you started...
TorrentSpy -> http://www.torrentspy.com/
The Pirates Bay -> http://thepiratebay.org/
ISO Hunt -> http://isohunt.com/
MiniNova -> http://www.mininova.org
Finally, I have had great luck finding unknown artists by using an NNTP News Server. NNTP is an old Bulletin Board type of protocol. NNTP means Network News Transport Protocol. But the NNTP community has evolved into about 50,000 different 'channels' that cover every imaginable subject and there is a way to 'encode' binary files to place them on these NNTP groups. For music, music is grouped into different 'genres'. For example, I download Jazz and Reggae from two different channels. It is not easy to find any particular song or artist, so I just download everything in a group and often find songs and artists that I've never heard of before.
To download music from NNTP groups, you'll need a News Reader. There are some free ones out there. I use this one...
http://www.newsbinpro.com/
Well, that ought to keep you busy for a while! Good luck!