Copy your ENTIRE iTunes FOLDER to The External Drive...
Full Details Here > http://support.apple.com/kb/HT1751
It is important that the External Hard Drive is formatted as Mac OS Extended (journaled).
And also make sure that all is working to your Satisfaction before Deleting anything off your Mac
For instance would it all work if I simply dragged the "iTunes" application to my external?
Yes providing you use
and allow iTunes to Manage your music.
Once you are positive that the External is working to your Satisfaction you can Delete your iTunes Library off your computer.
Leaving the iTunes Application / Program installed on your computer...
To Operate iTunes from the External Drive...
Start iTunes with the Option key held down and Choose library... and select the iTunes folder you copied to the external drive.
On Windows, hold Shift, launch iTunes and select Choose library... and select the iTunes folder you copied to the external drive.