Choose either the Audio or All Types categories (often, the All Types will give better results if you're looking for rarer files).
Now, just type in artist & song title... click search & there it goes! When the Lime's spinning, it's searching.

If you're not finding what you're looking for, vary your search terms a bit or try just searching for the album that the song is from. There's a little bit of info in the user guide here
http://www.limewire.com/english/content/userguide.shtml

Remember that people in different time zones will be logging on & off all the time, so searching at different times of day will give you different results.

If you're going to use the All Types, try using terms like
artist name - song title