First of all, there's no such thing as a free music download
site. Any site which actually hosted copyright music files on their servers would soon find that they were facing multi-billion dollar law suits.
Free (and usually illegal) music downloads are achieved through a number of peer-to-peer networks. With these networks, your PC is connected directly to someone else's PC, not to a central server.
The most popular network is Gnutella. There are various software 'clients' which enable you to connect into the Gnutella network. The most popular is Limewire. (i.e. Limewire is a program, not a website). Some people like it but others prefer alternative clients, such as Morpheus, FrostWire, Shareaza or Bearshare.
Links to all of the clients which can connect into Gnutella, are here:
http://www.gnutella.com/connect/
Gnutella's main rival network is eDonkey. Some Gnutella clients (e.g. Morpheus and Shareaza) can also access eDonkey. However, by far the most popular client is eMule:
http://www.emule-project.net/home/perl/general .cgi?l=1
Many people recommend a third network, BitTorrent, as being technically superior. The most popular client for accessing this network is probably BitComet:
http://www.bitcomet.com/
Shareaza might be a good program to try, because it can connect into all three networks.
Chris