To see counter steering of a two Wheeler in action, ride a bicycle without using your hands and go around a turn.
As you shift your weight to the inside of the turn, you see the front wheel first make a quick flick to the OUTside of the turn, immediately followed by it falling into the turn.
Tadah. Counter steering taken care of all by itself.
Oh, don't try this if you aren't already comfortable riding a bike without using your hands, both in a straight line and around a turn. :)