First of all, it's a commercial activity, and your home/neighborhood zoning may not permit that kind of activity.
Second, assuming you are zoned for swimming lessons, your homeowner's insurance may not cover business activities, so you would have to speak to your insurance broker about the extent of your coverage.
Third, you'd have to check with your local licensing bureaus (or an attorney familiar with this area) to see whether you need to be licensed to give swimming lessons and, if so, how many children you could safely teach and monitor at one time. You might be required to bring in extra staffing if you're planning on teaching more than one child at a time.
Nina L. Kaufman, Esq. is an award-winning New York City attorney, edutainer and author. Under her Ask The Business Lawyer brand, she reaches thousands of entrepreneurs and small business owners with her legal services, professional speaking, information products, and LexAppeal weekly ezine. She also writes the Making It Legal blog.