Unplug the microwave from its power source or, to be extra cautious, turn the power off in the kitchen while you're working.
Remove the access panel on the microwave, if there is one. Sometimes these panels can be popped right off, while other microwaves have screws that need to be removed before the panel.
Unscrew the bolts or the screws, depending on the microwave, that are holding the microwave to the cabinet above. If you have somebody helping you, it is a good idea to have that person hold the microwave while you remove this. This will ensure that the microwave won't fall down when loosened.
Slide the microwave off of the mounting brackets that are holding it in place. Since each microwave is different, this process will differ depending on your personal model.
Remove any mounting brackets or screws that remain on the walls or cabinetry. Turn the power back on in the kitchen if you turned it off when beginning.