If your ceilings have water damage, you need to remove the drywall and let the inside of the ceiling dry out. If you don't, mould might grow inside your ceiling. Fix the initial cause of the leak to prevent future damage. If you are unsure where the leak is, ask a professional roofer or plumber to examine your home. If you notice mould developing anywhere in your home, hire a professional mould-removal contractor to eradicate it immediately.
Push gently on the area to determine the extent of the water damage. You will have to remove and replace any sections of drywall that are mushy or severely bowed.
Use a utility knife to score a line around the entire damaged area.
Hit the area inside the score lines with a hammer to break the drywall. Remove all the damaged drywall.
Reach inside the hole to find the wood studs nearest the hole's edges. Use the utility knife and hammer to remove the drywall up to the studs, leaving a square or rectangular hole in the ceiling (having a squared-off hole will make it easier to fit a new piece of drywall). Then remove some drywall over the lengthwise half of the studs on either side of the hole (leaving half the stud exposed allows you to install screws there in order to attach the new piece of drywall).
Set up fans and dehumidifiers to dry the area inside the ceiling. If the air outside is dry, open the windows and doors to let in fresh air. Depending on the extent of the water damage, it could take several days for everything to dry completely. The goal is to avoid mould development after you close up the ceiling. Do not proceed until you are sure the inside of the ceiling is dry.
Cut a new piece of drywall to fit the hole. Use drywall screws and a screw gun to attach it to the wood studs. Install screws every four to six inches. Install screws along the outside edges of the hole where you uncovered the wood studs. This will reinforce the joint between the existing ceiling and the new piece.
Finish the drywall as normal. Use a six-inch drywall knife to spread joint compound over each joint. Place a section of paper drywall tape over the compound and wipe it smooth. Fill all the screwheads. Wait for the joint compound to dry fully (typically 24 hours). Then use a 12-inch drywall knife to apply a second coat of compound over the entire area, this time leaving a thick, smooth coat. Allow it to dry, and then sand the area with 150-grit sandpaper.
Prime and paint as normal. If you notice rusty or yellowish water stains showing through the joint compound, use a special hiding primer (available at hardware stores). Ask the staff or check the label to verify the primer is specifically designed to hide water stains.