It's amazing how many people don't understand counter-steer, and they'll just say, "oh you just lean the way you want to go!"
Anyone that can successfully ride a bike, is counter-steering whether they realize it or not. Most of us have been doing it since we learned on bicycles as kids.
There's a certain speed where counter-steer takes over, maybe 25+, not sure. We all know to turn the bars in the direction we want to go if we're at 10mph or slower in a parking lot.
Had a friend that kept wrecking bikes. He brought one to me saying it wouldn't turn. I rode it, it was bent, since he's already wrecked twice, hit a car once, and a chain link fence. He told me about trying to turn and the bike just goes straight. Had him describe his actions, and he was turning right to go right above 25mph. He didn't understand what I told him about steering, but he finally gave up riding bikes. Watched him in my mirrors once, went straight off a turn and stopped 4" from a drop into acreek..
One way I describe it to people... Push on the right hand grip to go right, push on the left to go left. Once you understand counter-steer, you can quickly dodge almost any obstacle in the road, potholes, roadkill, mufflers, etc. You need to be careful about snapping the bars though, some bikes will go right into a tank slapper at the right speed.