Here is a quick & dirty summary of the way I do it, using the ~/Music folder as the example.
1) Backup, backup, and backup whatever data is in question, as a safeguard.
2) Install and format the external disk, (preferable as 'OS X Extended (Journaled)' For this example, label it 'USB'.
3) On the newly created USB volume, create a subdirectory called 'Music'.
4) Move everything from ~/Music, (the Music sub-directory in your home folder), to the new 'Music' folder on your new USB volume. When satisfied everything copied OK, delete everything in ~/Music, (the Music sub-directory in your home folder).
5) Open Terminal and type: sudo rm -rf /Users/yourname/Music
6) Then type this in Terminal: ln -s "Volumes/USB/Music" "Users/yourname/Music"
Then open your home folder in the Finder. You should see what will look similar to a Windows shortcut for the Music folder, (a folder with an arrow at the bottom of the icon). While that resides in your home directory, when you open it, it should redirect you to the 'Music' folder on your external USB drive, (or whatever alternate location you chose).
A symbolic link (aka symlink) like this is a great solution because you do it once, with no need to change anything in iTunes. Say you buy a new song, it will download to ~/Music, but really follow the symlink and go to your USB drive.
I have done this 50 times, so I know it works, provided I understood your goal correctly!