Pretty much how modern ones work: with feedback control.
A specialized compass was invented in 1904 that allows to find the direction you’re flying including the change of height.
That information is compared to where you want to fly (spoiler: horizontally) and the difference is fed to the steering gear of the plane.
That technology was known from steam engines wich use the same technique to keep the RPM stable (with a centrifugal valve that opens more the faster it spins)
The only real difference is that today we do it in a microcontroller and not mechanically
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