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I have seen a documentary about making BGM-71 TOW (an anti-tank missile - the Iranians make it). You can see it in this link (part 1). Between 6:08 to 6:40 minute of clip, you can see a gyroscope. I would like to know how this gyroscope works. How did they connect it to their electronic circuits?

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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).

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