Measure the height of the microwave.
Measure up from the bottom of the inside of a cabinet to the height of your microwave plus 1 inch. Using that measurement, make a series of marks along the inner walls of the cabinet and along the back of the cabinet door.
Place a straightedge across the marks and connect them with straight lines.
Unscrew and remove the cabinet doors.
Unscrew and remount the first shelf from the bottom so the bottom edge of the shelf lines up with the pencil lines inside the cabinet.
Saw off the bottoms of the cabinet doors, along the marked lines. Sand the cut edges with 220-grit sandpaper.
Stain and finish or paint the cut edges to match the existing finish of the cabinets.
Cut a hole in the bottom of the cabinet, near the back, to thread the microwave cord through. Cut the hole with a hole saw.
Replace the cabinet doors. The removed sections will leave a opening at the bottom of the cabinet for insertion of and access to the microwave.
Place the microwave in the cabinet opening, threading the cord through the hole.