To repair a small hole in drywall, patch the hole with metal drywall patch, a wallboard joint compound, sand the surface, prime and then paint the surface. Use metal drywall patch, a wallboard taping knife, a drywall joint compound, a drywall sanding block, paint and primer to complete this task.
Start by peeling and sticking the metal drywall patch into the hole, and follow up by applying three layers of the wallboard joint compound on the patch with the wallboard taping knife so the compound extends about 6 inches from the edges of the hole outwards. The extension creates uniformity between the repaired hole and the rest of the drywall. Allow the compound to dry, and use the drywall sanding block to smooth the surface. Using a sanding block helps get a flat surface, which may be impossible when using a hand and sandpaper. For better results, reapply the compound, and sand again.
Once the surface is sufficiently smooth and flat, apply the primer, and allow the surface to dry. To achieve a uniform texture, use a small roller fitted with a medium nap. Check the surface to ensure it is completely dry, and apply two coats of paint, allowing the paint to dry between the coats.