Electrical connections to a rotating part?

...how people wire up multiple electrical contacts through a bearing or to a rotating sensor?

I would think the general answer is they don't. If you think along those lines and explain a bit more what you want to do - perhaps you can get ideas on avoiding the wires too.

E.g. if all you want to do is sense or synchronize rotation - you can put a small magnet on the rotating part and sense it passing with a stationary hall effect sensor (similar to how a car's anti-lock brakes work).