Move all furniture and home decor out of the room with the falling ceiling. Spread drop cloths over the floor.
Put on safety glasses, a dust mask and gloves. Place a ladder under the sagging ceiling and pull the affected area by hand to expose the rafters.
Square the broken out portion of the mobile home ceiling by cutting it out with a drywall saw. Measure the square hole in the ceiling using a tape measure. Then measure and cut a drywall sheet to the same size using the tape measure and drywall saw.
Fit the drywall piece into the ceiling and fasten it to the rafters with a screw gun and drywall screws.
Fasten drywall tape over the edges of the drywall patch, concealing the joints between the drywall and existing mobile home ceiling.
Cover the drywall tape with joint compound, using a putty knife to spread the compound over the tape evenly. Let the compound dry according to the manufacturer's suggested drying time thereafter.
Fit medium-grit sandpaper onto a sander and sand the drywall patch along with the compound. Then apply a coat of primer, using a paint tray and roller. Let dry, then paint the drywall with ceiling paint to finish.