I was an Aquatic Director, lifeguard, swim instructor, competitive swimmer (and related positions) for over 25 years (overlapping of course).
Babies can be introduced to warm water from birth on. Most swim programs (parent/child) start at 6 months. Parents are taught songs, movements, and ways to hold their children to maximize security and independence while they explore.
Depending on how your child takes to the water, if lessons are given consistently from infant and up, and children are exposed and allowed the time to explore, most children will begin swimming independently (no flotation devices) by around 3-4 years old.
The more comfortable parents are around the water, the more likely your child will learn to swim early on. I think it's essential that children learn to swim--enough to save themselves should they end up in a body of water. Children can drown in a shallow plastic kiddie pool!
at 7:35 AM on Jul. 23, 2009