Quit iTunes then drag your entire iTunes folder to another volume. This usually exists immediately within your Mac's Music folder. Be sure to copy the entire iTunes folder and its contents.
Next time you launch iTunes hold an Option key while opening it. iTunes will ask you to locate your music library. Navigate to your external hard disk drive (if that is where you decide to keep it). iTunes will remember its location.
Don't start iTunes unless the external volume is mounted and available, otherwise iTunes will revert to its default location. If that happens just use the Option key again.
When you are certain everything has been copied and everything works as you expect, you can delete the original iTunes folder.
Be sure to have a backup strategy for the external hard disk drive, as you would for anything you do not wish to lose.
iTunes: How to move [or copy] your music [library] to a new computer [or another drive] - http://support.apple.com/kb/HT4527 - a somewhat bewildering and not always easily understandable set of options.
Quick answer if you use iTunes' default preferences settings: Copy the entire iTunes folder (and in doing so all its subfolders and files) intact to the other drive. Open iTunes and immediately hold down the Option (alt) key (shift on Windows), then guide it to the new location of the iTunes Library.itl file in the moved iTunes folder.
For the record there's this reference for iTunes 11 but it really doesn't strike me as having the specifics you need. iTunes 11 for Mac: Move your library to another computer - http://support.apple.com/kb/PH12168