Due to the fact that water flows, it can sometimes be very difficult to find the source of a leaky roof. A damp patch on a ceiling will indicate you have a leak, but it's finding the source of the leak that's the tricky part.
Water may come into the roof through damaged or faulty flashing, cracked or broken tiles or even through faulty mortar on a side elevation. When you are trying to find the source of a leak, it's much easier if you can gain access to the roof space. If you can't do this, the job becomes infinitely more complex.
Assuming you have access to the roof space, it's first important to find the point at which the drip is leaving the rafters or joists. If the damp patch is at the edge of a room, the water may even be running the whole length of the rafter before coming into contact with the ceiling. If you find a drip, follow the tell-tale damp line back to the point of entry. You will usually see some staining which can help in your investigations.
When you locate the leak, you can take appropriate action to replace the faulty tile or fix the flashing. Or you can even just phone a qualified roofer who'll use the right roofing supplies to fix the problem.