We did swim lessons last year shortly after my daughter turned 4. It was 12 sessions. They really made a lot of progress! I am eager to start again next week (she's 5 now) and see how she improves this year.
After the first round last summer, she got comfortable doing short swims with her face under the water, back and forth between an adult and the steps. Heading toward being "water safe" (they really emphasized water safety and talking to the kids about pool rules and stuff). I personally did not feel she was "water safe" after last summer because I think she would panic quickly if she fell in or lost steam trying to swim. BUT she started the sessions just sitting on the step, not wanting to put her face in, and they got her actually swimming forward with her face in and keeping herself bouyant.
They warned us we would be backtracking this year because they would have forgotten everything they learned last summer... but MIL has a pool and has been working with her so is she right where we left off.
It really was an amazing process to watch (I thought)... there were a couple lessons in the middle that really seeemed brutal, like they were pushing the kids to the limits of their comfort zones, and it was tough to watch. But suddenly it clicked and the kids all just took to it.
Our swim lessons were in a private home, by a mom and grandma who have been teaching the local kids for years. Like, people my age learned to swim there and now their kids are learning to swim. The mom's sons hop in the pool and help out too (10 &12) so it's a family affair. They were awesome.