Here's a learning process you can do on your own at your local pool, lake or ocean. The problem with learning to swim is that there are perhaps a half a dozen independent motor skills needed and it's hard to learn them all at once. This breaks it down to one skill at a time. Do all of this is shallow water, say, four feet in depth.
1) buy a mask, fins and snorkel set.
2) throw way the snorkel (not really, store it away for much later)
3) start with a kick board and fins. Do an hour of just kicking with the fins on. Now you've learned the kicking motor skill.
4) Next put on your mask (defog it with your spit, youtube will show you how, yuckky I know but necessary) and now, with fins on, start kicking, as usual, but also start stroking with your arms. Don't bother trying to breath yet, just stand up when you need to breath. Do this for an hour.
5) Repeat 4 above but now try to breath on your dominate side (right side if you're right handed, other side if you're not). It's tricky to learn how to breathe without coughing, definitely practice this for an hour.
6) Take off your fins and repeat step 5. It will feel really weird without the extra power of the fins but your arm strokes should pull you thru.
7) Perhaps the ugliest part. Take of your mask and repeat step 6. Learning to manage the discomfort of having your face in the water does take some effort, but at least you've saved the hardest for the last. Keeping water out of your nose requires a continuous but very low pressure exhaling thru your nose when it's underwater. Your eyes will sting when you open them underwater so only do that for short glances to get your bearings.
8) Repeat step 7 for 32 lengths and bingo! You're a swimmer.