Raise and lock a sheetrock jack into place within 6 to 8 inches of the ceiling by setting the height latch lock.
Pry the loose, bowed sheetrock off the ceiling joists using a prybar while standing on a stepstool. Most of the sheetrock will remove in chunks and land on the sheetrock jack. The removed sheetrock will leave ceiling joists exposed.
Pull all exposed nails out of the exposed ceiling joists using a claw hammer.
Unlock the sheetrock jack's height latch lock and allow the jack to lower.
Dump the debris on sheetrock jack into a trashcan.
Raise a panel of sheetrock up to the ceiling joists using the sheetrock jack. Because you removed entire sheets of sheetrock, you can fit the new sheetrock panels into the open space.
Nail the sheetrock into place using the sheetrock hammer and sheetrock nails.
Nail the remaining sheetrock panels into place using the sheetrock jack, hammer and nails.
Swipe sheetrock mud into the seams between the sheetrock panels using the putty knife and the pre-mixed sheetrock mud. Wipe excess mud away using the flat edge of a putty knife and allow the mud to dry for 24 hours.
Press a strip of sheetrock tape into place along the mudded seams.
Swipe a 1/4-inch layer of sheetrock mud over the edges of the sheetrock tape using the putty knife and sheetrock mud. Use just enough mud to cover the tape's edges or you risk tearing the tape and having to re-tape the seams. Allow the mud to dry for 24 hours.
Re-mud any cracks that appear as a result of the mud drying and allow the mud to dry for 24 hours.
Re-paint your ceiling using matching paint and a paint roller.