Counter-steer, is that like turning into the direction of the skid in a car to get straightened out?
On a bike it is : Push right to turn right. Push left to turn left. This does not apply when "walking" a bike through a parking lot....sitting on the bike doing the duck waddle at 2 mph.
Below 10 mph or so, you would turn the handlebars to the right and keep the bike upright.
Some riders do this instinctively, most need to be taught.