How does this kind of gyroscope work?
It is simply a gyroscope - meaning a flat spinning disk that has three axis decoupled through bearings for yaw,pitch and roll.  You need to read the common platform angular displacement from the mount to determine the amount of rotational movement.  So a shaft encoder on each of the axis'.  However, it's not as simple as that, as you need to consider precession and wind-down (loss of rotational speed due to friction).