To move just the content and not the library files, see:
IMPORTANT: do not delete the iTunes folder or the preference files it contains from your boot hard drive; delete ONLY the tracks themselves (i.e. the contents of the old iTunes Music folder).
You can also just drag the entire iTunes folder (the _entire_ folder, _not_ just the iTunes Music folder) to your desired location. Then hold down the Shift key while launching iTunes. You'll be given a dialog box where you can select the iTunes library you want to use. Navigate to and select the iTunes folder in it's new location. Note that this procedure assumes that all of your tracks are contained in the iTunes Music folder. If they're scattered around your volumes, moving them becomes much more complex. And don't launch iTunes with the external drive not mounted or iTunes will default back to the internal drive. If it does, though, just mount the external drive and launch iTunes with the Shift key again.
In either case, don't delete the tracks from the old location until you've confirmed that they're working correctly from the external drive.