Drywall Patching

You can use basic drywall skills to repair damage to your smooth ceiling.
If possible, check the space in the attic above the damaged area for wires or plumbing lines. Use a stud sensor to locate the ceiling joists and determine what direction they are facing.

Poke an awl through the ceiling around the damaged area to determine how far the damage extends.

Use a straight edge to mark the area you plan to remove, and use a drywall saw to remove the damaged area and any insulation from above.
* Most ceilings use standard 5/8" drywall; however, drywall is available in different thicknesses. Your replacement piece should be the same thickness as the existing drywall.
Make sure the replacement piece will have adequate support. If necessary, you can toenail a wood block between the joists for added support.

Use a utility knife to cut out a piece of drywall to fit the area you're replacing
Replace any insulation you removed earlier, and fit the replacement piece into the hole in the ceiling. Secure the drywall to the ceiling joists using drywall screws. The screws should just dimple the drywall rather than breaking all the way through the surface.

Apply a thin layer of joint compound over the joints and drywall screws, and apply a piece of drywall tape to the wet joint compound. Apply an additional layer of joint compound over the drywall tape and smooth it out with a drywall knife.

Sand the area smooth and apply additional coats as necessary. Sand between each coat.

When the area is dry and smooth, prime and paint it to match the ceiling.