More often than not, it is the shower drain pipe area which is leaking water down into the ceiling dry wall below. The problem usually is not with the black PVC plastic pipes though at times, the glue used to connect two PVC plastic pipes together could be beginning to deteriorate. If it is the latter case with the PVC pipes problem then it is best to call a professional licensed plumber rather than do it yourself. If it is just the draining area connecting your bathtub drain with the PVC pipes, then you could do it yourself.
1. Locate your bathtub drain flange.
2. Use a Screwdriver, Plier or drain key to turn and unscrew the drain connector.
3. Your bath tub drain then should look like this:
4. Use a bathroom silicon caulk and do the caulking around the edges of the hole. Let the caulking dry for over 12 hours or more. This step is not necessary but i like to be extra cautious making sure that this bathtub never leaks again.
5. Using a Teflon tape, put it around the drain body cover and put some "Plumber's Putty" over the edge of the drain body cover as in the picture below:
6. Screw the drain body cover back into the hole and tighten it with screwdriver, clamp, or drain key.
There you are, it is all done and your bathtub will never leak again unless the Plumber Putty gets old or the Teflon tapes wear out. Even then, the caulking that you applied on the edges of the hole earlier will prevent any future leaks guaranteed.