I think the original 'hard drive speaker' idea came from Afrotech a couple years ago:
Step 1: Open the Hard Drive
You'll end up seeing something like this.
Use a hacksaw to cut as far as you can between the hard drive arms and the platters. Then for the final bit of metal under the arms, use a dremel from the backside of the case. Don't worry about cutting through the flexible cable going to the arms, you should be able to see where the arm voice coil (the coil of copper wire between the two magnets at the arms base) is soldered to the which you're cutting.
Step 2: Solder on Wires
You might have to remove the top magnet to have easier access for soldering. To do this, drill out the screw heads keeping the magnet on from the other side of the case. Even then, the top magnet is pretty damn hard to get off, you'll have to pry it off with a screwdriver.
Then you might find it easier to solder to the coil ends if you pull the ends off of wherever they were soldered, this way the ends are free and not so close together.
Step 3: Play Music
It will only work if the thing is resting ontop of a good sounding surface, if you're holding it in your hand it won't work. This is like how the strings of a guitar won't make much sound without the big flat guitar beneath them.