Many times people look at the discoloration of a ceiling and figure that there is a leak right above those particular stains. They set themselves up on the roof and begin replacing the shingles right above where they believe the stains to be. This could be asking for trouble. Sometimes this may be the right thing to do, but more often than not, the leak is not where you think it is.
Water finds its own way out, and that applies particularly to the escape path from inside the attic. The water may enter through a soft opening, or where there is insufficient roofing material. It can even be from where the nails have rusted, and are exposed. The water passes through the wood deck, and into the attic. Once in the attic, the water may travel along the roof trusses. This is where the problem of detecting the leak can lie. Once the water begins traveling along the trusses, it could end up most anywhere, and it would be difficult to find the trail of water along the truss.
Following the water line requires some degree of expertise, or at least a sharp eye. Since the trusses are made of a higher grade of wood than the deck, or other parts of the attic, they will be less inclined to leave clues where the water has traveled. You can track the water with patience, keen observation, and a good flashlight. Find as best you can the entry point. From there, even though the trusses may be a higher quality wood, there will still be clues. Follow the water using gravity and common sense, and you will see the entry and exit trail of that leak.
When you find the entry point, you can mark this spot by driving a small thin nail through the deck to the surface. If the nail is long, or odd colored, it will be easier to spot when walking around on the roof later. From there, you can assess the damage, and decide what should be replaced. When completed, it's always best to test the area for other leaks. Sometimes you can hold a hose where the leak was, and see if it continues to leak. Sometimes you just have to wait for the next rain. There is no real easy way to patch a leak, but patience and attention to small details will have you spending less time than if you guessed at the location of the leak.