Frame the opening with four 2-by-4s. Measure the length of the top and bottom of the wall opening. Cut two 2-by-4s to fit the top and bottom. Place the bottom 2-by-4 flat and centered in the bottom of the vent opening. Attach the 2-by-4 with 3-inch screws along the center line spaced at 4-inch intervals. Measure each side of the wall opening. Cut two 2-by-4s to fit. Place each 2-by-4 flat and centered against the side of the vent. Screw in each 2-by-4 the same way as you installed the top and bottom 2-by-4s.
Measure the rim of the vent hole opening on the interior side of the wall opening -- not the interior of the 2-by-4s. Cut a sheet of drywall to fit. Place the drywall over the interior vent opening. Install a 1-inch screw at each corner of the drywall into the 2-by-4 frame.
Seal the gaps. Fill the narrow space between the drywall panel and the edge of the wall opening with joint compound applied with a small trowel. Place joint tape over the filled gaps and smooth it in place. Apply a thin layer of joint compound over the joint tape. Use the remaining joint compound to fill in the depressions in the drywall sheet made by the screw heads.
Cut insulation to fit and place it inside the vent opening, with the paper side facing the interior. Do not compress the insulation.
Measure the rim of the vent hole opening on the exterior side of the vent hole -- not the interior of the 2-by-4s. Cut a sheet of plywood to fit. Place the plywood into the exterior vent opening. Install a 1-inch screw at each corner of the drywall and into the 2-by-4 frame.
Cover the exterior and interior of the repaired area with siding, shingles, stucco, paneling or the appropriate material to match the surrounding wall. Seal the seam between the old and the new covering with caulk if necessary. Add a new layer of paint over the entire wall to disguise the repair.