Locate the power cable for the microwave and unplug it.
Open the cabinet above the microwave and locate the mounting screws connected to the top corners of the microwave.
Remove the mounting screws with a flat-head screwdriver.
Take one end of the microwave, and tell a partner take the other end. Carefully lift the microwave off of its rear metal mount.
Place the microwave on the counter. You can now replace it with a new microwave. The detached controls are likely connected to the current microwave remotely.