Go up on the roof. Check for tears, cracks, rotting areas, missing sheathing, and any other potential issue. Also check for breaks in material such as no spaces between the brick of the chimney and the roof sheathing. Put an object by each problem spot so you can find them again later. Pick an object that won't blow away.
Go into your attic. Look for any potential water trails with a flashlight. If you find any, follow them up to where they hit the ceiling and push a nail at that point so you can easily find the problem spot when you get back onto the roof.
Repair cracks in the sheathing. Clean the crack by scraping away any dirt. Cover the crack with roofing cement and use a trowel to cover the crack completely. Lay down a piece of roof patching fabric slightly bigger than the crack. Cover the fabric with roofing cement. Repeat for all cracks. Follow the instructions that came with the roofing cement about how to mix and apply it.
Repair breaks in materials such chimney bricks and roof sheathing. Clean the area and remove old pieces of cement that may become irksome. Work a layer of cement between the roof feature and the sheathing. Spread the cement into the sheathing. Repeat for all breaks.