Sand the area. Use a hand sander to sand out the area that appears to be damaged. Use a coarse sanding paper such as 40-grit or 60-grit.
Re-attach the drywall. Water damage may have cause the drywall to sag and if this is the case, re-attach it in place by nailing it against the joist. A joist is a beam that runs horizontally to support the roofing structure of a house. If the area is larger, be sure to use more nails.
Seal the drywall. In order to prevent the water damage from bleeding through, apply a primer to seal in the moisture and color.
Paint over. Use a paint roller and mix some drywall compound with water to use as a coat to paint over the repaired area. Let it dry and then use another coat of house paint and paint over to blend in with the rest of the ceiling's color.
Prevent the leak. To prevent further water damage, pin point the cause of the water damage, most likely a leaking air-conditioning vent, and fix it.