Consider removing furniture in the affected area and propagate a plastic sheet on the floor below the marked walls and ceilings. It is always recommended to put on safety gloves and glasses to prevent yourself from harsh substances. Goggles are also considered very important when performing this kind of job because you will be applying the chemical to the ceiling where it could drop on your face or eyes.
Firstly, you will need to mix 1 part water with 1 part bleach. Now dip the sponge or a cloth into the chemical solution and rub it over the marks or stains on the wall. This will eliminate any mold or pattern growth and reduce the dirt.
Now consider spraying some clean water from a bottle to get rid of the bleach based cleaner. Dry the area using clean cloths and leave it to dry before you start putting paint on it. Apply some stain killing solution or chemical to the affected area of walls and ceilings. It is recommended to use mildew or mold-fighting solution if the area you are working in has been affected by mold patterns.
Now let the coating dry completely and then apply one or two layers of ceiling and wall colour paint to match the entire area. Let the paint on the walls or ceilings get completely dry before removing the plastic sheet or covering.