With that out of the way, let's get into it!
First, you want to snip the AC wire at the top of the lamp, about an inch from where it goes into the head. You can now pull it out of the body of the lamp.
Now, select a drill bit for your drill that's just around the same size as the head of the two silver rivets that are holding the lamp head onto the arm.
Awesome! I'd save the head of the lamp for another cool project. We won't need it here! Last bit for the lamp for now. The oval bracket that was holding the head before is slightly curved (to be flush with the lamp head), so use your needlenose pliers and straighten it out.