How do you determine where your roof is leaking?

You'll have to look underneath from attic side when its raining, then when dry look in area to see roof damage.

If you have access to attic., go there and look for wet areas or water stains.

Water tends to find the path of least resistance. If you have an attic. Have someone be in the attic. Take a garden hose with no nozzle. Pour water on the roof in small areas. Start at the bottom work your way up. When it starts to leak in the attic you found the general location. Most of the time I have found flashing around pipes and vents that needed to be sealed.

What William says. Water travels to the lowest point so where the water stain is may not be where the water leak is. Walk the roof to see lifted or rotten shingles.

Everyone here has the right idea but in all seriousness, call in a roofer. They understand leaks and where the source will probably be. I have a flat roof over my sunroom and it had a leak for years. One roofer actually found the place that allowed water in (not anywhere near the dripping, ) fixed it, and I haven't had another drop of water in my sunroom since 2011...