Unplug the microwave power cable.
Open the microwave door and insert the tip of a putty knife or small flat-head screwdriver in between the plastic interior panel of the door.
Work your way around the frame until it pops off. This will expose the internal metal frame of the door.
Insert the tip of your putty knife or screwdriver into the seam where the metal frame meets the door. Work your way around the frame, popping the internal clips as you go. This will release the frame and you will have access to the latch.
Tighten the screws on the latch assembly with the Phillips screwdriver to secure it to the door. If the latch is damaged beyond repair, you'll need to replace it.
Remove the screws holding the latch assembly in place with the Phillips screwdriver and remove the assembly.
Fit a new assembly in the old one's place and replace the screws.
Snap the door frames of the microwave back into place.