Simple ? iTunes Question

Following an external HD failure I am reloading iTunes from a back-up HD. Problem is as I re-enter the album back to iTunes it is loading the music into my iMac. I want the music to stay in the external HD and just play from there. My internal HD GB available count is dropping faster than a speeding bullet.

What am I doing wrong? iTunes settings?
I'm not sure this solves your problem but you do need to specifiy the location of the iTunes music library if you want it stored somewhere other than the default, which would be the internal drive on you iMac.

Open iTunes and select 'Preferences' under the 'iTunes' menu at the far left of the menu bar on your iMac. Then click on the 'Advanced' icon at the far right in the Preferences dialog box.

The top box shows the current location of your music library, probably something like, "/Users/yourname/Music/iTunes/iTunes Music. If you want it elsewhere click the 'Change...' button and navigate to your external hard drive.

Here's more detail from the Apple support pages.
Just hold down the Option key while you start iTunes and it will show you a dialog box to switch library or create a new one on any drive you want.
Well, I was able to move the library per your suggestions BUT much of the music remains sitting in my internal HD as well as in my external HD. I tried deleting an album in the internal HD but as soon as I pull the same album up again in the external HD it downloads it back into the internal HD so I don't need the external HD on to play the music. Before that was impossible.
Puerto - It's hard to diagnose your issue from a distance but I suspect what you need to do is start over with the import process.

I tried to duplicate your situation by installing a fresh copy of OSX on a clean hard drive, which includes the iTunes application. I also attached another external hard drive to represent the one you want to have as your music repository.

I then booted up the computer from the external hard drive with nothing but the fresh operating system on it, opened iTunes and went through the process I described above to put the iTunes music library on the second hard drive.

I inserted a CD, dragged the music files on it into the open iTunes window on the boot hard drive, waited while they were copied and then checked their location. They were copied to the second hard drive, the one I had chosen via the iTunes preferences. Playing them from iTunes on the boot drive worked perfectly.