Simply, you have 3 sensors - one in each axis - which are "zero'd" when you engage the autopilot. By this I mean that any output from them at this point would be taken as the null condition.
And deviation from that null will produce an output from the sensor, which is then used to drive a flying control surface. This will cause the aircraft to change attitude, and the output from the sensor would return to it's null output state.
This is real simple, and there's many improvements, including rate systems, which means that the rate of chage is detected, so the correction is applied at the same rate as the disturbance.
To get the autopilot to do something more usefull than just 'cruise control' you can force disturbances on it, and the system will react as if the aircraft had changed attitude, not just the gyro platform. The early Hercules uses this system. Quite simply, there are small motors which move the platform, and the sensors react as for a normal aircraft disturbance.
Hope this helps.
ps. try doing a seach for Mk10a or 10b autopilots.