Find the studs in the wall area behind the stove using a stud finder. Mark the studs with a pencil and a straightedge.
Measure out the wall or walls within 36 inches of the wood stove. Reduce the height by two inches to accommodate the space for air ventilation behind the heat shield at the ceiling and at the floor. If you are building a partial wall, reduce the measurement by only one inch for the bottom gap.
Cut a section of 1/2-inch asbestos millboard for the back of the wall, using a utility knife. Wear a dust mask when cutting the millboard and cut outdoors to keep any asbestos dust from entering your house.
Cut 26-gauge sheet steel to fit over the millboard using aviator snips. Cover the surface of the millboard with construction adhesive using a caulk gun. Use a zigzag pattern to cover about 60 percent of the surface. Attach the sheet steel to the millboard. Allow the glue to dry for the time recommended by the manufacturer.
Screw 1-inch metal spacers into the combustible wall using 2-inch screws. Space them every 12 inches in a grid across the wall.
Set several 1-inch-thick sections of wood or masonry temporarily at the base of the wall. Set the heat shield against the spacers and on top of the temporary blocks with the aid of a helper.
Screw through the sheet metal and the millboard with 3-inch drywall screws using an electric drill to attach the heat shield to the wall. Space the screws out along the studs every 18 inches. Pull out the temporary blocks at the base of the wall.
Attach a layer of metal lath over the sheet metal with self-tapping 1-inch screws every 16 inches. Cut the lath with tin snips or aviator snips.
Mix mortar and water in a 5-gallon bucket with a trowel. Make the mixture damp enough to hold its shape on the trowel but not so wet that it drips. Cover the metal lath with a layer of mortar, smoothing the surface evenly with a 12-inch trowel. Dry the mortar overnight.
Mix another batch of mortar and use a 1/4-inch notched trowel to cover a small area of the heat shield wall. Butter the backs of tile or brick veneer and set into place on the wall. Continue laying the veneer, use tile spacers to keep the tile evenly spaced and use a level to keep them straight.
Dry the mortared veneer for at least 24 hours. Pull out all the spacers. Use a mortar bag to squeeze mortar between the bricks or grout between the tiles. Clean off any excess with a damp rag and smooth the joints with a jointer tool.