How do I find the leaks

I take it that the sink is upstairs... if there is not an obvious leak under the sink that you can see then the leak will be in the wall behind sink which flows across ceiling or the drain pipe runs across ceiling and has developed a leak. The ceiling needs to be fixed... you could cut hole to find out source and see how bad that cast iron drain is. Write back. I live in Toledo if you are close then help is close... walt