Unplug the microwave's electrical cord from the outlet, which is typically inside the cabinet on the back wall above the appliance.
Remove the bolts in the bottom of the cabinet above the appliance, using a flat-head screwdriver. Use pliers if the bolts are not slotted. Recruit your helper to hold the appliance steady while you work.
Push up on the underside of the microwave slightly to disengage the lip on the back of the appliance from the wall's support bracket.
Lower the microwave gently to the range top, pausing to pull the electrical cord through the cabinet hole where it was routed to the power outlet.
Take out the screws or bolts holding the bracket on the wall above the range. Save this hardware if you wish to reinstall the appliance at a later date. If you are replacing the microwave with a different model, use the hardware that comes with your new appliance.