Insert drywall screws through the center of plaster washers.
Climb the ladder to reach the area where the plaster is coming down.
Screw the washer into the plaster and the lath behind it. The lath is small wooden strips holding the plaster in place. Try locations in the ceiling until you hit the lath. You can patch the holes later.
Spread joint compound over the cracks in the ceiling once you have inserted washers and are sure the ceiling is secure. Use enough compound to cover the washers. Spread with a plaster hawk, and then smooth out.
Place screen mesh, such as a piece used for screen doors, over the compound and press it in slightly.
Spread more compound over the mesh and smooth out. Taper down as you move out past the repair onto the original plaster. Wait a day for it to completely dry.
Sand down bumps with 220-grit sandpaper and add more compound with a trowel to any low areas. Let it dry again and sand smooth.