You'll need to drill out the old rivets (unless someone has replaced them with something different) under the outside door handle.
Remove the inside door panel by removing the 2 plugs in the arm rest and unbolting those 2 screw, and remove the screws in the diagram below .
Reach inside door and unhook the rod from the outside door handle and then remove the outside door handle like in the diagram below
You'll need these rivets like these to replace the rivets you drill out to remove the handle. 1979-93 Mustang Door Lock Actuator Rivet at LRS - Same Day Shipping!
I suggest you have the body shop install the new rivets because it takes a large rivet gun to install the 1/4" rivets.