I took lessons at the Lions Pool on Tuesday evenings the summer I was eleven, mostly because my cousin was already going and my mom wanted us out of the house. The chlorine smell still gets me more than anything else from that year. An instructor kept telling us to relax, which never told me what to actually do differently, and I spent most of that summer coming up gasping before something about the breathing finally clicked. I couldn't tell you which week.
Your first day
Starting takes standing in the shallow end with goggles on and repeating one thing five times.
Face in the water, blow out slowly through the nose the whole time, count silently to ten, stand up and breathe in through the mouth. Repeat five times total. Then, only where you can stand up and with a lifeguard or friend watching, push off the wall and glide face down for a second or two, without kicking or pulling yet, still breathing out slowly.
Don't hold the breath underwater the way it feels natural to. Holding it is what causes the panicked gasp at the surface. Breathing out steadily the whole time underwater means the only thing left to do when you come up is inhale, calmly, because there's no held breath to burst out.
The thing most people miss
Nearly all of my early panic in the water traced back to breath timing, and almost none of it to my arms and legs. It took most of a summer to notice, because everyone talks about the stroke.
Once I practiced the exhale-underwater, inhale-at-surface rhythm on its own, completely separate from any stroke, the rest of swimming stopped feeling like an emergency I was managing. The strokes I'd been so worried about turned out to be the easy part, sitting on top of a breathing pattern I hadn't actually learned yet.
What not to do
Don't skip goggles to save money on day one, chlorine stings enough in the first week to wreck focus on its own. Water up the nose is the other real blocker nobody mentions, and it goes away by exhaling harder through the nose, not by pinching it or tipping the head back.
Swimming turned from something that happened to me into something I was doing on purpose, the moment breathing quit being the thing I fought against every length. That same shift is waiting in the kick too. Most people never learn the power is supposed to come from the hip, not the knee, because nobody ever tells them to check.