I taught Parent-Tot swim lessons, as well as lessons for older children, from 1988 through 1996, and started my ds in the water at 2 months (much to the alarm of my pediatrician). He loves the water, and starting learning to swim on his own at age 3. Children can learn to swim as early as 2, although retention of the skills is better from age 3 on (no danger of having to re-teach).
I wanted to mention two things. First of all, no matter what a lesson program tells you, your children will not be drownproofed! It is impossible to completely "drownproof" a child, which is why most public swimming facilities require parents to be in attendance with children under the age of 12, regardless of how well they can swim. I was a lifeguard for a number of years, both at pools and open water (lakefront, and oceanfront) and I can tell you that there are many situations that can arise in which good swimmers drown.
Secondly, if you decide to take your infant swimming, keep in mind that swallowing too much pool water can lead to hyponatremia, a condition in which the electrolyte balance is thrown off. This can lead to serious consequences, including hospitalization and, if not treated, can be fatal. This can be avoided by never forcibly putting a child underwater.
Most YMCAs have good parent-tot programs that are more water adjustment and bonding with parents, and start actual lessons at age 3. For older children, the YMCA program is excellent, as is the Learn-to-Swim program run by the American Red Cross. It usually last 1-2 weeks in the summer, and cost is nominal. For you homeschoolers, most states allow swimming lessons to fulfill a phys ed requirement.
I am an advocate for swimming lessons for all children, and highly recommend that all parents involve some form of swimming instruction and water safety into their parenthood.