Hi,
We did one semester of babyswining. It was fun but I guess my girl didn't learn to swin on her own.
The things I remeber that we did was:
Hold the baby under his/her arms or let the baby lay on one of your arms (and you hold your hand around the babys arm near the shoulder/armpit, the parent walk/turn backwards when you do it this way) and pull him/her around in the water while the baby kicks. Kind of the beginning of swiming.
When you do this above you can have a toy (that flotes) and make the baby "go fetch it".
You can also hold the toy under water and let the baby try to grab a hold of it (distans looks different in water).
You can have a floating madrass (don't know the real word for it) and practise jumping of it (holding the baby under his/her arms all the time) We did this and put the babys head under water and pulled them up at once (don't know if you can do this with an older child).
ANother thing we did that the teacher told us was very important that a baby/child can do, is to jump into water and then turn and grap a hold of the ledg and pull himself up out of the water. We practiced this by letting the baby sit on the side of the pool (holding on to the baby under his arms), saying 123jump and then helping the baby to jump into the water and at once turning the baby around and making them grab a hold of the poolside and helping them get out with a little puch on the put or leg or foot.
We aso had one of the floating noodles (or what you call them?) and letting the babys body rest on them on the armpits near the chest, the parent then pull the baby fast in the water (parent going backwards).
I usualy did all of this in water were I have the watersurfas somewhere under my sholders. But this eas individual.
Good luck with swining and ask questions if you dont understand

All the best
Bellan