Select a location for your microwave oven that is large enough to accommodate its width. Check with a stud finder to ensure that there is a stud behind the location to support the microwave's weight.
Turn off the electricity to the kitchen. Cut an opening in the cabinets sized to the ducts you will use above or behind the microwave installation site with a rotary tool saw attachment, being sure to avoid studs and wiring. Cut a corresponding opening into an existing oven duct, or directly through the kitchen wall or ceiling.
Insert a straight length of metal duct into the space between the new openings. Select a duct that is the appropriate width as noted in the microwave's installation guide -- 3 1/4-by-10-inch rectangular or 6-inch round ductwork is common. Add duct elbows and adapters to create a path between the site for the microwave and the opening in your kitchen wall or ceiling. No more than three 90-degree elbows are recommended. Crimp the joints between duct components with a metal crimper to seal them together.
Fit and crimp a roof cap or wall cap outside your home where the duct exits through a finished exterior surface. Seal around the cap with caulk to prevent air and moisture from leaking into your home.
Measure the space where you want to install the microwave with a tape measure. Mark the wall with a pencil based on the manufacturer's installation instructions. Screw in the microwave's mounting brackets using a screwdriver.
Slide the microwave into position and attach the interior end of the duct as you lock it into position. Attach a damper adapter, if necessary, so the microwave's vent leads directly into your microwave's duct. Plug in the microwave and test it by running the heat function for a few seconds. Check for loose duct components or installation problems if you feel warm air coming from the microwave.