If it is plasterboard you can bodge it yourself if you want. You will need a small hammer, some short, galvanised plasterbiarding nails, and a cartrdge of solvent-free grip adhesive with a gun (metal not plastic) some Easifill, and a broad metal filling knife.
You clean away all the dust and fix up the bits like a jigsaw then smooth over once the adhesive is set and it is rigid. While setting, press a flat board, wrapped in clingfilm, up from underneath, braced with a deadman.
Or ask around and get recommendations for a local plsterer. It will look better if you get the whole ceiling skimmed.
Plaster dust is very damaging to carpets, soft furnishings and electronic apparatus, especially computers, televisions and DVD players, and domestic hoovers.
What sort of hoover have you got?