Learning how to swim backstroke is something you can teach to yourself. Backstroke swimming's most critical element is... wait for it... you swim on our back.
Yes, I know, not an astonishing swimming secret, butif you are not comfortable laying on your back in the water, backstroke can be tough to master. You need to get that skill figured out first, then you can move on to learning actual backstroke.
Practice laying on your back, gently kick (any kind of kick for now) and try to get your body "on top" of the water, or at least parallel to the surface of the water, with your face out, nose pointing up. It can help to imagine you are pushing your belly and/or your hips up to the sky. Try to look up or even slightly backward. The goal here is to get your body up in the water, not find the perfect body position. Yet, anyway - that will come with more swim practice.
1. Backstroke Body Position
As mentioned above, backstroke body position is parellel to the surface of the water; your head position can control what happens. Think straight line from the top of your head, down your spine, and make that line parallel to the water's surface. Your nose should point up toward the sky/ceiling. Your shoulders should be rolled forward, making your back slightly curved, like the bow of a boat.
Start this by getting on your back and push off of a wall, get in the parellel position and put your hands on your thighs, arms straight; roll your shoulders up and in across your chest, keep your head back, nose up, with the water at about your ears. Keep practicing getting in that position from a push off of a wall until you feel comfortable.
2. The Backstroke Kick
The thing to remember for backstroke kicking is make a lot of bubbles; make the water boil by your toes. Kick with relatively straight legs, kick more from the hips, relax your ankles, and go, go, go. If your knees come out of the water you are letting them bend too much.
Push off the wall, get in the parallel position, hands on your legs, and curl your shoulders in, and start kicking. And kick. And kick. Remember to keep track of where you are in the pool, don't hit your head on the wall.
3. Backstroke Kick and Body Roll
Once you are good at kicking while laying on your back in the parallel position, you begin to add in some body rotation. While you are kicking, lift one shoulder out of the water, let the other shoulder drop under water - keep your parallel line parallel - keep your head laying back, nose pointing up - keep kicking - then switch shoulders.
Kick with one shoulder up for 3-10 kicks, then switch to the other shoulder up. Repeat. Repeat. Repeat.
Hopefully you are seeing the pattern here. Work on each swimming skill until you are comfortable, then move to the next one. If you move on to the next skill, and then feel like you are losing the previous skill details, no problem. Go back a few steps and start again.
Hmmmmm. Your face is out of the water at all times. When do you breath when swimming backstroke? More or less whenver you want! One typical pattern is to breath in when one arm is up in the air and blow out when the other arm is up.
5. More Kicking and Body Rolling
Now change the arm position while you kick. Keep one arm at your side, put the other up, pointing where you are going. If you were standing up, it would like you were holding your hand up to ask a question. That arm's shoulder should be rotated down a bit - the bicep is just under your ear. The other shoulder (attached to the arm by your side), should be up, out of the water, almost touching your chin. Remember to keep your head still and your nose pointing up.
Kick, kick, kick. This is like freestyle 10/10 drill, only upside down.
Switch arms by moving the arm by your side up, in a big rainbow arc through the air, and swap locations with the arm that was up - that arm goes down by your side by moving underwater in a big arc.
6. The Arms - Pulling in Backstroke
The basic pull is a straight arm that exits the water thumb first and enters the water pinky first. This is not the best backstroke pull, not like you might see at the Olympics, but it is the easiest way to learn it.
While you move your arms (pull), you always keep each arm opposite of the other arm. If one arm is going in the water (pinky first) the other arm is exiting the water (thumb first).
When an arm is in the air, its shoulder should be the one that is up and out of the water. The arm in the water's shoulder should be the one that is down, in the water. Your shoulders (and your body) rotate above and below the water, along your parallel line, with your arms. Remember to keep your head still and your nose pointing up. And kick!!!!
7. Swim Backstroke
Keep the kick going, keep the arms going, and breath. Still head, nose up, shoulders rising with their atached arms. You are swimming backstroke. Congratulations. Try doing some backstroke during your next swim workout.