There's a couple of systems but basically they (in real time) detect & instantly reverse the movment causing the image to shift. Some "counter vibrate" the lens guts & some "anti-wiggle" the sensor to reduce the effects.
You watch in real time, its not a recording.
more info here in detail.
http://www.picturecorrect.com/tips/h...lization-work/
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Allan Quatermain: “Automatic rifles. Who in God's name has automatic rifles”?
Elderly Hunter: “That's dashed unsporting. Probably Belgium.”