On a flat roof with a waterproofing membrane, or IBR sheet roof, leaks can occur when the membrane fails or where fittings rust over time, allowing water to gain access. In houses with pitched roofs, leaves may collect in the valleys between peaks, causing a build-up of debris which will stay damp. The first indications of these are normally damp or wet walls, or stains on the ceiling.
For small areas, there are a variety of commercially available products that you can buy to remedy the situation. Larger repairs are best left to the professionals, as the process involves the use of a bitumen product that is heated as it is applied to the roof surface.