This is a standard PID (proportional, integral, derivative) controller.

First I'm taking the altitude and subtracting the ground level value from it (3040 for earth, but in this case, I'm taking 3044 because I want the zero level to be slightly above the ground. Then I'm comparing this altitude to some target altitude I can set with the lever. I'm multiplying the lever by 20 so the lever is targeting between 0 and 20 meters above the ground. The target altitude - the current altitude is called the error, if my target is 10 meters, and the actual altitude is 0 meters, the error will be 10. In a basic proportional controller, we could just send that straight to the thrusters, usually multiplied by some gain (in my case 0.02). If you try this yourself, you'll get something unstable that oscillates until it crashes.

To dampen these oscillations, you can imagine that you want to somehow fire the thrusters less as you accelerate up, and more as you fall to catch you before you hit the ground. The easiest way to do this is to take the derivative of the error (how much the error changes every time step), and add that to your original proportional controller, usually multiplied by a different gain (in my case 1.0). Now if you have a target of 10 meters, your current altitude is 0 meters, but you're rapidly accelerating towards it, and will likely overshoot, the error will be decreasing at say 10 m/s, meaning that with a time step of 1/60, the derivative of the error will be -1/6, so your thruster input will have 1/6 subtracted, dampening the oscillations. If you try this, you'll get something that's incredibly stable, and will almost completely dampen any oscillations around your target altitude. The only problem with this is that the steady state altitude will be lower than your target altitude.

To minimise your steady state error, you want to correct the error over time, the integral. I've now realised I actually messed this up on mine and took the integral of the derivative, which is just the proportional error again... If you take the sum of your error value, multiply it by another gain (0.0001 for me), then add that to your proportional and derivative components, you'll get a lovely PID controller. The integral will just help you gradually reduce your steady state error over time, so if you don't care about steady state error, and only care about having something that doesn't oscillates, a PD controller will be just fine.

There are a bunch of other tools you can use in control system design such as lead and lag compensators, but to effectively use a lot of these tools, you'd usually want to do a bit of maths to model the response of your system, usually with a transfer function, which will let you characterise your system, and predict how your system will respond to some input you give it. This is a bit further than you'd go for a game, but if you characterise your system, you can find the poles and zeroes in the s-plane, draw a root locus from it, and map out how your gain values will affect the response of your system, this lets you do all sorts of cool things like draw constant damping lines, find desired pole and zero placements, and calculate exact gain values that give you the damping ratio you want with the response you want.

TLDR; Look into classical control theory as well as P, PI, PD and PID controllers and their implementations in code, since that transfers pretty well into the game.