Starting iTunes differs for Mac and Windows.
For Windows: Start iTunes while hold down the Shift Key.
For Mac: Start iTunes while hold down the Option Key.
iTunes will then allow you to "Create Library" or "Choose Library". Depending on what you want to do select the appropriate button. In my case I simple click "Choose Library" and then select my external hard drive.
All this is straight forward and it seems you understand this part of it. The other part not often mentioned is you must go into the iTunes Preferences and under Advanced set the iTunes Media folder location. In my case the external HD is named iTunesMusic and my entry looks like this: /Volumes/iTunesMusic/iTunes. Make sure the check boxes for "Keep iTunes Media folder organized" and "Copy files to iTunes Media folder when adding to library" are both checked. Click OK and that should do it.
The above description only works if your external drive has been set up as an iTunes Library by first using the "Create Library" option mentioned above.
I hope this is of some assistance to you. I have been working with iTunes in this way for several years with no issues. I must note though that I am using iTunes 10 not the newer 11. I just don't like 11 and it took me several days to get my system back to version 10 after installing iTunes 11.
Good Luck