You might check in your local community to see if Infant Swim Rescue (ISR) is available. It’s a valuable tool and well worth it if it’s offered in your area.
We always paid for swim lessons for our kids but we are lucky as there are many young folks on the college swim team here that offer services. That’s another opportunity too if there are any swim teams in your area.
If you do go ahead on your own, my advice is to take it slow and be patient. The biggest challenge and hardest thing to learn for a kid that young is to get their face wet and be comfortable going underwater. So you have to play games with them to teach them how to feel ok with putting their face in the water. Keep them on a ledge that is their height and tell them to blow bubbles like a fish. See how long they can do it for. Then keep making it longer each time. Also get lots of play toys like plastic rings and under water torpedoes and such. While learning to swim is an admirable goal, 3 years old is still a bit young for that. Teaching them to float on their backs, grab the coping for a safety-hold and pulling themselves up and out of the water is going to take a long time.
My youngest is 6 and has been in the water for 3 years. My oldest is 17. All of the kids are competent swimmers but it took years of practice and lessons to get them there. It won’t be done in one summer.