You can remove mold from ceilings and walls with a mixture of 1/2 cup bleach, 1/3 cup powdered laundry soap and 1 cup of water. You'll need to scrub with a sponge in a circular motion and let dry. Be sure to wear gloves!
Try using bleach in a corner of the room where it wont be seen. If there is no damaged, try to remove the rest of it. It may be caused by a leak in the attic, or the floor above, check that after removing the mold.
If your ceiling is made of a porous material, such as sheetrock, then removal and replacement of the ceiling will be necessary. Mold cannot be removed from sheetrock.
Mold is not easy to remove and can cause a lot of health problems. Areas need to be taped off and every piece has to be disposed of properly. You will have to have air ventalation masks, because breathing the mold spores can cause serious health conditions. It is best left to a professional.
