TBH, I think it's easier to send them to lessons. I find that when I take ds's all they do is splash about and do jumping in but ds1, who is now 4, has been going to lessons only since last May and is practically swimming on his own now because he'll do things formally for a teacher that he won't do when he's with me.
She uses 'discs' (I think they are National Swimming Association but not sure) - they start off with 3 or 4 on each arm and she gradually takes them off until they have none. They are so good I even bought my own for taking the kids myself even though they cost about £8-9 each!