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Snap a chalk line or use a carpenter's square to form a rectangle that encompasses the damage. To protect sound plaster from damage while clearing deteriorated plaster from the rectangle, screw plaster washers just outside the chalked lines.
Score the plaster along the chalked lines with a utility knife; then, with a hammer and cold chisel, remove the damaged plaster within the rectangle, chiseling gently to avoid loosening plaster outside the rectangle.
Cut strips of 1/4" plywood, 1" wide. Edge the opening with the strips, loosely fastened with 1-5/8" drywall screws driven partway into the lath. Shim the strips to position a scrap of drywall flush with the plaster. Tighten the screws. Trim the protruding shims with a keyhole saw.
Cut a piece of drywall to fit the rectangle. Depending on the thickness of the plaster, use 1/4", 1/2", or 5/8" drywall. Apply a bead of construction adhesive to each plywood strip, then press the drywall against the adhesive. Fasten the drywall to the plywood strips with 1" drywall screws 6" apart, starting at the corners.
Cut pieces of mesh drywall tape to cover the edges of the patch, and press them into place. Using a 6" or 8" drywall knife, spread joint compound over the tape, just thick enough to cover the tape. Do not wrinkle the tape. Allow the patch to dry for 24 hours, then apply a second coat, feathering the edges. Once the patch has dried, smooth it with fine-grit sandpaper on a sanding block, feathering the edges. It may take 3 or 4 coats to get a perfectly smooth patch.