To be honest most of the basic physics behind rocketry actually isn't too difficult. The matter of engineering it into reality definitely is very difficult, finding fuels that burn hard enough and figuring out how to contain them while they burn and the like. The nature of going so far and so fast also means that tiny errors add up to very big problems.

All rockets function on the fact that if you push something in one direction, you also go in the opposite direction by a proportionate amount. Lighting fuel on fire while it's in a tube that only has one way out just happens to be a great way to push the burning fuel really, really hard and therefore get a really hard push back. The forces involved always have to cancel out the total momentum of everything involved; you chuck X kilograms of burning fuel out of the back at Y metres per second, you accelerate forward by however much you need to to make your momentum match that in the opposite direction. This is Newton's third law of motion, the "for each action there is an equal and opposite reaction" one

Nozzles and the like can adjust which direction the way out is pointing. If the way out points left a bit, the momentum of the fuel is also going left a bit, so the reaction momentum you get goes a bit to the right, and now you have steering

I think the biggest conceptual block people usually have about orbits is that they're not about going up fast, they're about going around the Earth fast. If you point your rocket straight up and just keep going straight up, you won't go into orbit around the Earth. Either you'll crash straight back down when you run out of fuel, or you have a rocket with enough power and fuel to reach Earth's escape velocity, in which case you'll just continue travelling away from Earth forever until you find something else's gravity. You know the kind of arc that a ball has when you throw it? Imagine that you're superhumanly strong and can throw a ball literally however hard you want. You could throw it beyond the horizon without breaking a sweat. Once you're throwing it that hard, the curvature of the Earth starts to become relevant, right? The ground is effectively dropping away underneath the ball as it travels forward, letting it fly farther before it hits the ground. Eventually if you throw hard enough, the curvature of the Earth turns away from the ball at the same rate as the ball is falling. The ball is now in orbit. The ISS (and anything else that wants to orbit at the same altitude) goes around the Earth so fast that it does 15 entire laps around the planet every day

Unfortunately for our rockets, the Earth's atmosphere is very bad to actually move through that fast, so they go up first to get out of the thickest part of the atmosphere and then gradually turn sideways to achieve orbit

Once you start getting into things like how to get from Earth to other planets you've got to worry about some other stuff, but this comment is probably getting long enough by now and not many of our rockets do that yet

I totally get what you mean about planes not looking like they should work. The size of them and the fact that we've got basically nothing to reference them against for scale and motion when they're in the air is really confusing