Remove the furniture from the room. Spread tarp or plastic sheets on the floor to protect it from damage.
Setup a sturdy stepladder on the floor directly under the falling section of the plaster ceiling. Drill 3/16-inch holes every 4 to 6 inches through the falling plaster, and into the wood lath underneath.
Vacuum the debris using a shop-vac. Spray water into the holes to soften the plaster and prepare for a strong adhesive bond.
Insert acrylic adhesive through the holes using a caulking gun. Apply steady pressure on the trigger until you feel a slight bulge on the plaster. Wipe off excess glue around each hole with a wet rag.
Drive drywall screws fitted with plastic washers into the holes to draw the falling plaster back to the lath. The plaster adhesive oozes out through the holes in the drywall screws. Allow the plaster glue to set for the time specified according to manufacturer directions, as each brand has its own curing period.
Spread joint compound over the ceiling, directly above the repaired area using a trowel. Use enough compound to completely cover the washers.
Cut a section of insect mesh screen the size of the wet compound. Spread it over each repair section and press it lightly so it adheres to the compound. Smooth the screen with the trowel. Let the compound dry for 24 hours.
Smooth out high spots on the repaired section with 100-grit sandpaper. Wear a dust mask so you do not inhale the residue. Rub the surface of the repaired section so it blends with the surrounding plaster surface.
Prime the repaired section with a paintbrush and leave it to dry. Apply two coats of paint over the repaired section to match the tint of the surrounding plaster ceiling.