First, you need to realize that there may be some restrictions such as having to listen to the music only on your computer rather than being able to transfer it to your mp3 player. If you want to put the music on cds or an mp3 player, you may need to just give in and purchase the music. If you are not extremely picky and just want to listen to some good tunes, look at the following steps!
Visit websites like pandora.com, new.music.yahoo.com, music.aol.com, and free.napster.com These websites have streaming music online. You can pick and choose stations, choose artists you prefer, eliminate artists or songs that you dislike, or just listen to a genre of music. You cannot download this music in order to listen to at a certain time later, but you can revisit the site and listen to your chosen stations whenever you want. Please realize that these stations are available to the public for free because of advertisements. You may have to deal with a 15 second ad every couple of hours. The free music is totally worth it though!
Search for a free downloading software such as Q-trax and E-Ztracks.com. There are others, however many of them provide music by independent artists who do not have a major record label. Some popular songs will be available, but some will not. Q-trax, a new service, has deals with the major record labels and will be adding songs to their database starting in 2009.
Look for your local radio station's website online. Many radio stations provide a streaming version of their radio station so you can listen from anywhere, even if you do not have a radio nearby! You can still participate in call-in contests but be aware of the 1-2 minute delay that the online station may have from the radio.