Watch this video from This Old House to learn how to patch drywall.
1. For tiny holes and popped nails, use 4-inch drywall knife to apply two or three thin coats of joint compound.
2. Allow each application of compound to dry, and then sand, between coats.
3. Repair small- to medium-size holes with an adhesive-backed aluminum drywall patch.
4. Peel off the protective backing to expose the adhesive, then press the patch to the wall directly over the hole.
5. Coat entire patch with joint compound, then use 12-inch-wide drywall knife to smooth the compound.
6. Allow the repair to dry, then sand smooth and apply two or three more coats of compound.
7. For large holes, cut a piece of drywall slightly larger than hole.
8. Hold the drywall patch over hole and trace its outline onto the wall.
9. Cut along the pencil lines with a drywall saw.
10. Cut two 1x2 cleats slightly longer than the size of the hole.
11. Apply construction adhesive to the cleats, then slip them into the hole.
12. Position a cleat to each side of the hole, making sure each extends into the opening.
13. Attach the cleats to the wall with 1 ¼-inch drywall screws.
14. Set drywall patch in place screw it to the cleats.
15. Spread joint compound over the drywall patch.
16. Press a piece of insect screen into the wet compound.
17. Force the screen into the compound with a drywall knife, then spread more joint compound on top.
18. Let the repair dry, then sand and apply two or three more coats of compound.
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