>>>CAVEAT... After typing all this, I suddenly realized this assumes you have a PC, not a Mac. Similar principles should apply in the Mac environment, but this assumes a PC...
Let's see, you *copied* the songs from your main drive to the external drive, right? What format are they in?
Here's the general overview. iT has a library file that is basically an XML database that has info in it that has been read from the file tags (if available) and notes re: which playlist the song appears in, the playcount, etc. If you are OK with losing all that, you can just nuke the iT database file and then "add folders to library" specifying your external drive as the folder to add.
Here's why this might be a bad idea... You *will* lose all your playcounts and playlists. If you use a file format without tags--such as WAV--you will also lose all the album/artist/genre info, since that is *only* stored in the database for WAV files.
Here's another potential slip... iT has a feature called "keep my music organized" which will copy all the songs to where iT thinks they ought to be when you add them. So, even if you move them, if that flag is checked in iT, you will end up having all the files moved *back* to the iT default directory, which is probably *not* your external drive.
So what can you do? You can actually use the iT "keep organized" function to move the stuff for you. If you have copied the files, nuke 'em. Then reset the iTunes library to the external drive and check the "keep organized" button. That should result in all your files moving to the new external drive, organized into Artist/Album directories.
In the vein of potential slip ups... if you succeed in doing what you want, iT will have a new library where all the pointers are to a drive (specified by a letter). When your external drive is mounted, you need to make sure it appears as the same letter each time. Probably not that big a deal, but if you have a digital camera and turn that on before the external drive, you may find the digital camera memory as F: and the external drive as G:. If you turn them on in the reverse order, the external drive will be F: and teh camera G:. While you won't care, iT won't be able to find the files in one of those cases.