I got Hendrix at 4 and a half months old and he was started in water within the week. It's important to get them used to it early, or they may never enjoy it. I didn't let him swim until 6 months, and even then I've only recently allowed him to go out more than two or three strides.
It's really up to you and him when you start.
If you can start him in shallow water where he'll only get his paws wet, perfect. After that you could start throwing his toys in so he goes in up to his belly to get him used to the feeling of pushing through water, ect. I don't think there should be an age limit on swimming, but puppies under 9 months should be very carefully supervised and should only do light exercises, water work is very tiring.
Personally, I allow Hendrix around 20 entries into the water at max, and these are all very short swims. This is around the time when he begins to tire, but not long enough that he is getting tired enough to pose any danger to himself.
At first this was only 3 entries, none of which involved more than a single stride, if that. Hendrix had been worked fairly easy and has grown a lot of confidence because of it. My rule was always to never push him, but now that he's gone totally crazy about swimming and never refuses a throw, my rule is: KNOW WHEN TO GO HOME
A young puppy will also need to build up fitness. Hendrix runs with me and swims every second day, but to begin with this was a walk to the river so he could put his feet in, then home again. Everything in moderation. Your pup will tell you when he's ready.
I've had 21 dogs in my life, and this mongrely poodle has been one of my favourites. No regrets on getting the stupid little dog with the messed up eye. He's been funner than the perfect dogs.