Adjust the flow, buckets and load. The wheel settles where water torque equals the millstone load plus friction. Buckets fill at the top, hold water on the way down and spill it before the bottom.
The science
Bucket torque. Water arrives at a fixed flow Q. Each bucket then carries m = ρ Q (2π/Nω), so faster rotation means less water per bucket. Water stays in the bucket until a spill angle and then leaks linearly to empty near the bottom. Summing m g R sinθ over the buckets on the descending side gives torque τ = ρ Q g R K/ω, where K is the geometric integral over the loaded arc.
Power. Because τω = ρ g Q R K, the power taken from the water does not depend on speed until the buckets overfill (then torque saturates). The efficiency ceiling relative to the full head 2R is K/2.
Steady speed. The wheel obeys I dω/dt = τ(ω) - τload - bω. At steady state bω2 + τloadω = ρ g Q R K, giving a unique speed. If the load is too large for the bucket capacity the wheel stalls.
Simplifications. Water enters with negligible speed and impact loss, bucket shape and splash are ignored, the flume has no head loss, and tailwater drag is not modelled. A real overshot wheel reaches 60-85 % efficiency.