Removing the odometer is simple, pretty straight forward and self-explanatory. The replacement odometer can be set identically to the original odometer with precision - it's just a matter of knowing what you're doing. There is a small clip that holds the clock movement center shaft into the frame of the odometer, and it slides out once the clip is removed. Be aware that the seal, which is a flimsy plastic strip, is easily damaged, so be careful with that. New ones are not available...this seal provides alignment of the numeric wheels and is the part that breaks when someone tries to force the numeric wheels to read a non-legitimate number.
The movement itself is a series of number wheels. Each wheel is designed to index the one to the left of it once for every full rotation of itself, incrementing the numeric readout. There is also a ratchet style mechanism in each wheel that prevents the number from decrementing itself, which would prevent the odometer from going lower when driven in reverse.
The design is pretty reliable, and if you have problems where the speedometer MPH indicator works when the odometer doesn't, it's usually attributed to a defective driven gear.
On the analog cars, the trip odometer frequently wears out, preventing the digits from resetting to all zeros. You can feel and hear the "rusty" sort of noise when you push the reset knob, which is an indication of wearing parts within the odometer movement.