ok the easiest way is to go to prefferences under the edit tab in itunes, then go to advanced and change the itunes media folder location to your desired location (i.e. USB stick or external har drive). now click ok and go to
file --> library --> organize library ... this should give you an option to consolidate library .. check that box and click ok ..
this will copy all songs, tv shows, and apps to the location you described in prefferences .. just make sure your library is smaller than the location you are copying it to ..
The method you describe does not backup iTunes. Rather it makes new copies of the media files in a new location and connects iTunes to them. Take the USB stick or external har(d) drive away and the original library is broken, and the "copy" is also an incomplete library.
See this user tip for a proper backup regime.