This is what we are doing to get our 3.5 month old puppy to swim.
We take her to the beach when almost no one is there so it was nice and quiet. With her on her leash I walked her up and down the beach until she was finally walking in water.. We walked a little deeper and deeper very slowly for about 10 minutes until eventually she could just barely touch. We stayed there for while with her. Then I took a step out where I knew it would be just over her head and she tried to walk to me got a little paniced at first but she just starting swimming a bit and she swam back to where she could reach.. Then we would call her to us after a minute or two (giving her time to forget) and we repeated that for about 20 minutes.
Eventually she just swam up and down the beach, with me right next to her. We haven't been in deep water yet but she knows now she is close to the edge so she isn't nervous about it anymore. Eventually, I will lead her out a little farther and farther as she gets more comfortable.
Hopefully that helps.
