Hi there,
I recently had the same issue, and here's how I solved it.
First, make sure the USB-drive is connected.
If you hold down the option key while clicking the iTunes button, a menu will open. This menu will allow you to Select or Create a library.
I basically used this option to create a new iTunes library on the external disc (just browse to the location). And I enabled the iTunes options "keep iTunes media folder organized" and "copy files to iTunes media folder when adding to library" under iTunes preferences -> advanced.
Also note that you can set the location of your music folder here. This also means that the first step of creating a new library is not strictly necessary (you can just change the location of the media folder in the preferences), but this step ensures that iTunes will not mark songs as "unavailable" if you forget to plug in your USB drive before launching iTunes.
The downside of moving your library file to the external drive, is that iTunes will not launch if the external drive is not connected. (Instead, it will say that the library cannot be found, and the same menu -asking you whether you want to select or create another library- will open.
Hope this clarifies things a bit.