I took ds1 from when he'd had all his jabs, so about 4 months. I've heard that they don't say yo uhave to wait anymore, so ds2 has been swimming every week since he was 8 weeks. So I now take a 2 1/2 year old and a 3 1/2 month old swimming on my own every Tuesday afternoon!
I heard the thing about the head dunking before I first took ds1, but never had the guts. However, he would hold onto me and squirm, and sometimes would get splashed, or go under. If he ever did, I would be careful not to appear shocked, but to carry on as if it was part of our play. He seemed to just take to it naturally and is now a real waterbaby! Ds2 doesn't squirm so much when I hold him, but gets splashed by his big brother, and again I'm careful not to react. On the odd occassion when it has upset them, though, I've done huge huge cuddles, and got out if they've needed it.
The pool we go to is great - it has a kind of beach section so when I just had a toddler I would just sit while he splashed around me. Now with the two we go out a bit deeper so that ds2 sits in the baby float and ds1 can throw himself around. I started him in armbands very very early on, at the stage when he couldn't answer back! Now he just accepts them. The baby float is good because you have hands free time, and you can get better eye contact to soothe the baby, and you can walk up and down the pool which is almost as good for you as swimming!
Sometimes we go to an ordinary pool. I have never used the steps. With the baby I lay him by the edge of the pool while I quickly get in, and then pick him up. When ds1 reached the rolling stage I still did this, but put his feet pointing towards the pool. When he reached crawling stage I could still move fast enough. As a toddler he sits on the side with his feet dangling in while I sing humpty dumpty. By the time I get to "fall" I'm already in the water holding my arms out!
I've gone on a bit, I'm sorry! I just love my swimming sessions so much. Finally, the beach pool is incredibly cold. When ds1 was tiny we used to get out when he started shivering! But I've bought one of those uv suits (looks like a little wetsuit) and ds2 wears that over his swim trunks, and can stay in for ages - it seems to keep him warm enough.
Good luck, I would definitely go again. Such good fun!