The best article I've seen regarding counter steering, and how practicing it can help one improve their skills and avoid a road hazard or crash. And look, it's about bicycles, not motorcycles!
You must steer the handlebars in the opposite direction you want to turn.That means steering the bike toward the danger first!Remember in the second paragraph, I said that don't even think about "turning" left to avoid the car. Well, you aren't turning left, you are "steering" left. This will cause the bike to fall away from the car toward the direction you want to turn.Basically, you are forcing a lean instantly instead of waiting for it to happen naturally as in a normal turn.Then you steer the handlebars back in the direction of the turn to complete the process.The most common mistake here is to over steer back after the initial steering input.Another common mistake is cramming on the brakes while trying to turn quickly.Both of these actions make the bike straighten out and become upright too early.You want to continue the turn until you have safely turned inside the turn of the car.The point to remember is that you will always lean (or fall) away from the direction you steer the handlebars.
The quicker and more forcefully you do the initial counter steer, the quicker and sharper the resulting turn. Go try it!
Quick turn