To repair a leaky ceiling, repair the leak behind it, then patch or replace the ceiling. If the leak is small, the damaged portion can easily be removed and patched. Otherwise, more extensive repairs may be required.
Fixing a leaky ceiling is really two repairs in one. First locate and fix the leak — this could be a dripping pipe or an unsealed roof tile. Once the leak is found and fixed, the ceiling repair can begin.
There are many types of ceilings available for modern homes. Drywall and plaster, tin or drop ceilings are a few common options. Drop ceilings will be the easiest to repair; simply remove any panels that are damaged or have watermarks. Those marks indicate damage, even if there is no swelling of the tile.
Tin ceilings are usually drywall underneath, so the tin tiles will need to be carefully removed, although they might be reusable with a light cleaning. Any damaged drywall underneath should be cut away. To maintain as much integrity in the panel as possible, follow the seams to separate the damaged portions of the panel. Then if the removed portion is small — less than a foot square — a patch kit from the local hardware store can be used. Anything bigger will require a new sheet of drywall, cut to fit and nailed to the exposed studs. If necessary, replace any insulation; tape and mud over the seams as well. Recover the patched area with new plaster, or tin tile.