NORMALLY, the origin of the leak is much higher up the roof than where it shows through. Water will travel down a rafter, or something until it hits an obstacle then drops.
The best method of finding the leak is to go in the attic or crawl space above the ceiling with a flashlight and get in the general area and look for a dark stained line.
Once you find this water travel area, then you will see its origin and then stick a 8D finish nail through the hole or area then when on the roof you will see the nail and the area to start your leak proofing.
Yes, its important to stop the leak for many obvious reasons, but the secondary is to prevent rotting of wood under or behind the scenes.
Do not, attempt to fix the interior until you are absolutely sure the leak is fixed. The interior area must dry out completely before any repairs can occur.