If all you want to de is back up your music, you can simply copy the iTunes Music folder to an external hard drive. To do this, go to your home directory; if you open a new Finder window, this should be in the sidebar as a picture of a house with your name next to it. If not, open your hard drive (double-click the icon on the desktop), open the Users directory, and then open the directory with your name (or short name) on it. Open the Music folder, then click-and-drag the iTunes Music folder to the external drive. Wait a while (quite a while if you're collection's large) and you're done! If you need to restore from backup, just move it back to where it was.
Otherwise, we're assuming that you want to use your library from the external drive, which is a little bit more complicated.