Apply spackle around the area being patched with a spackle knife. If the hole is more than an inch or two wide, fill the hole first with a piece of drywall. Cut the drywall to fit and screw it into place.
Cover the hole with drywall tape. It should stick to the wet spackle. Smooth another coat of spackle over the tape. Allow it to dry for 12 hours, or until the spackle has turned white.
Sand the area until there are no ridges. Be careful when sanding over the tape, and don't remove too much spackle. Apply another layer of spackle and allow it to dry for 12 hours.
Sand and spackle again. It usually takes three coats of spackle to achieve a smooth surface.
Remove any dust with a tack cloth, or a damp cotton cloth. Paint the area in the same color as the rest of the ceiling.