Identify the areas of the wall, ceiling and soffit where the venting ducts will run. Ensure that these spaces have adequate room for the ducts.
Use your saw to cut a duct-sized hole in the back of the cabinet or wall close to the installed range hood.
Connect the range hood to the duct-sized hole using adjustable elbow ducts if the hole rests perpendicular to the range hood's upper vent. Secure this first area with duct tape and sheet metal screws.
Connect more ducts to the duct attached to the range hood. Run these ducts behind the wall or in the attic until you reach the soffit.
Run the duct straight out the side of the soffit by cutting a duct-sized hole with a saw. If you need to angle the vent down toward the ground through an overhang, cut a hole in the overhang and connect the horizontal duct to a vertical duct using another adjustable elbow duct or a transition fitting.
Cover the exposed exterior vent with a protective grille. Seal the edges of the vent with caulk.