If drywall on ceiling is wet and soft. Damage is beyond normal drywall repair, you will need to replace the drywall. This is usually the case with the above scenarios. Move furniture away from area and cover the floor and all areas with drop cloths and plastic. If the area has lead paint you should take more precautions to avoid spreading lead dust. Professional contractors must use EPA RRP guidelines.
Next use a drywall cutting tool to cut the damaged drywall out. It is best to use a square edge to pencil in a line along the beams and a 90 degree angle between the beams. (Create a square or rectangle shape with similar measurements that can be recreated with a new piece of drywall).Once you have penciled in the cut line, use the saw to cut drywall being careful not to hit any water lines or electrical lines. Once you get a few small pieces removed you should be able to see what is up in the ceiling. Next use a drywall knife to cut back drywall along the center of beam so that the new drywall and existing drywall can be secured to the same beam.
As a contractor I never know what I will find when I open a ceiling. I know what should be in a wall. But always be prepared for the unexpected. Sometimes you will have insulation that is wet. This should be removed and replaced. If you seal in a wet surface you will definitely have a mold issue in the future. At other times I have found water pipes and electrical wires placed to close to the drywall. It is best to cut a small opening first and take a look inside to be sure.
The end process is to have a level patch that once it is completed it will not be seen. After your cut out is done make sure you use the proper thickness of drywall. The most common mistake is to use the wrong thickness. The most typical is ½ in. and 3/8 in. It is important to get this right because if your new drywall is thicker, you will always see the patch and if it is thinner you will use an inordinate amount of spackle to make the patch level.