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Start installing from the bottom step. Apply construction adhesive generously to the existing stair tread. Place the first new stair tread securely on top of the existing tread. Then, apply a bead of construction adhesive along the top back edge of the newly installed tread and along the front edge of the existing step. Insert a small scrap wedge of wood behind the bottom edge of the new riser to provide additional support, ensuring it resists kicks. Apply construction adhesive to the back of the bevel-cut riser and secure it in place with a nail gun. Use finishing nails spaced evenly along the top and bottom edges. The construction adhesive provides the primary bond, while the nails hold the pieces in place until the adhesive cures.