Open the counter above the microwave oven and find the bolts that hold it to the counter. Have a friend hold the microwave up so that it doesn't fall down when you take out the bolts.
Unscrew the two screws on the front grill and remove it. In some models there will be levers that you can pull up to take off the grill.
Look inside and find the levers on the right and left sides. Turn these levers to unhook the microwave from the mounting plate. In older models there will be two long screws that look like small metal rods with slots cut in the ends. Unscrew these with the standard screwdriver.
Lift the microwave oven up and off the hinges. Let your friend help you as the microwave is pretty heavy and will probably be in an awkward position for your back. Take the microwave down and set it on the counter.