If you notice blistering or peeling paint, a discolored stain, or a bulge on your ceiling, it's likely that water damage has occurred. This can lead to structural damage and dangerous mold growth, so it's important to take action right away. The first step is to stabilize the area around the leak and catch any water that has accumulated. Most likely, the ceiling covering is made of drywall, which will absorb or disperse water.
To control where the water enters, drill a small hole in the center of the leak with an awl, screwdriver, or similar object. This will allow the water to pass through the controlled opening and reach a bucket. Next, you'll need to locate and repair the source of the leak. Water can travel a surprising distance from its initial point of entry, so it's important to be thorough in your search.
Roof leaks can be especially difficult to isolate, so if you notice water damage to the roof on the top floor, it's best to call a roofing contractor. They will be able to check if the roof is leaking and determine the best way to repair it. If you live in an area with high humidity levels, use a dehumidifier and vents to remove excess moisture from your home. This is especially important in bathrooms and kitchens.
You may be able to handle this on your own if you're good with that kind of thing, but most of us will need to call in a professional. Make sure that whatever is causing the leak is properly repaired or you'll have to face this problem again. Going to dry everything without repairing the leak and then continuing with business as usual is only a temporary solution.