Measure the microwave and determine how much space it will occupy and the position that you wish to install it. Determine how much of each cupboard must be removed for the microwave to fit in its desired position. Write this distance down as the removal distance.
Remove all cupboards affected from their position on the wall and completely disassemble them into their component parts. Remove all hinges, doorknobs and fasteners. Separate the pieces of the cupboard that are vertical, including doors, and set them aside.
Take one of the vertical pieces and make a mark that is exactly the removal distance from the bottom of the board. Turn that line into a mark drawn across the board with a yardstick or a t-square. Cut along the line with a saw and sand the new edge if necessary eliminating rough edges. Repeat the process for all vertical pieces.
Reassemble the cabinets and reinstall them in position, redrilling holes in the sides of the cabinet if necessary to attach the bases in their original positions with the original brackets or screws. Redrill holes for new hinge positions if necessary and attach the hinges. Redrill holes for new doorknob if necessary and attach the new knob in place.