Drill a hole through the drywall in the ceiling where the leak is coming through. Have a bucket handy to catch whatever water comes out of the ceiling. After whatever water is present has drained away, cut off any drywall that is damp or damaged. Leave the hole open so the interior of the ceiling dries out.
Find the source of the leak by examining all of the fixtures in your bathroom. Run the taps while observing the water pipes that lead to them. Flush the toilet and watch around the base for water leakage. Fill the tub and sink and then drain them while watching their drains.
Explore the underside of the bathroom floor with a flashlight. If you're lucky, this area is directly above the portion of ceiling that you cut out. If you're less lucky, you may have to cut out more of your ceiling. Sometimes water will leak in one place, travel horizontally inside a ceiling and come out the ceiling in another place.
Repair the leak when you find it. The method of repair that is required will depend on the material that is leaking. A copper pipe will probably need to have a section or a joint cut out and replaced. You may be able to repair a PVC drain with PVC adhesive, although a bad break or leak will probably require a new section of pipe.
Leave your ceiling unrepaired for a week or two after fixing the leak. If after that time there is no sign of water in the bathroom or inside the ceiling, it's probably safe to patch it back up with new drywall.