Flip off your circuit breaker to cut the power to your kitchen. This will reduce the risk of electric shock when uninstalling your microwave. Use a flashlight if it is too dark in your kitchen for safe removal.
Unplug the microwave from its power outlet. The power outlet will most likely be located in the cabinet just above the microwave and there will be a hole in the underside of the cabinet for the cord.
Remove the front access panel at the bottom of the microwave. You may need to unscrew some screws to get it off depending on the manufacturer, or you may need to just squeeze its sides and pull it off. Either way, it will expose the bottom of the wall mount bracket.
Have an assistant hold up the microwave from the bottom while you unscrew the screws underneath it, which connect it to the mounting bracket. The microwave will fall forward a little when you remove the screws.
Lift the microwave up off the bracket and pull it forward. It should come away from the wall and expose all of the mounting hardware underneath, like the brackets. You may now repair or replace your microwave. Repeat the steps in reverse order to reinstall the unit.