Open the microwave door by pulling on the currently installed handle.
Pry the door trim off of the interior side of the door by inserting a putty knife into the trim edge and gently popping the clips free from the door. Once the clips are free, you can remove the trim from the door, exposing the handle screws.
Remove the two screws holding the door handle to the door using a Phillips-head screwdriver.
Pull the handle away from the exterior side of the door to remove it.
Place the replacement handle onto the door, then insert and secure the previously removed door screws.
Replace the door trim back onto the door. Run your finger along the trim, applying firm pressure until you hear the trim clips snap back into place.