Drywall or plaster, the repair process is the same.
1- Remove any loose particles.
2- Check that the surrounding area is still firmly attached to the subsurface. If not remove any parts that are loose.
3-lightly sand the area to knock down any sharp edges.
4- Brush or vacuum the dust off.
5- Apply a coat of drywall compound to fill the void. All purpose is good. If you want to work quick you can use some "hot mud" that dries quick.
6- When dry, lightly sand again and wipe the dust off.
7- Apply another skim coat covering a wider area.
8- When dry sand lightly any high spots or ridges. Then wipe with a damp sponge.
9- (Your ceiling looks like it has a light orange-peel texture.) Spray the area with texture spray set on light to med-light. Spray in a spiral motion about 24 to 30 inches away from the surface to blend. Spray at least 6 inches outside the repair area. ( use plastic to cover a wide area on walls and the floor. Also practice on scrap cardboard or plastic, the initial spray from a new can is a large splurt. Don't spray that on the wall or ceiling.)
10- Allow to dry thoroughly. Then paint.