Cut away the ragged edges of plaster and wallboard from around the crack or hole, using a utility knife. Buff around the edges of the damage lightly with fine-grit sandpaper to smooth out any bumps or irregularities caused by the hole.
Mix powdered spackle with water following the package's instructions. Alternatively, use a ready-made spackle patching compound that doesn't require mixing.
Force spackle into small cracks and holes, using a spackling knife. Smooth the surface of the spackle by drawing the edge of the knife over the spackled area. Cover the crack with perforated drywall tape and press it into place using the knife.
Cover large holes with a drywall patch. Smooth a thin coat of spackle around the perimeter of the hole, using the spackling knife. Center the patch over the hole and press the edges into the spackle with the knife.
Smooth spackle over the tape or patch with the knife. Apply a thin coat that completely covers the patched area and extends out beyond the patch by 2 to 3 inches. Allow the spackle to dry for at least eight hours, then apply a second coat.
Sand the patched area lightly with fine-grit sandpaper to smooth the area, particularly around the edges of the patch. Paint over the patch with a paint color (and finish) that matches the surrounding wall.