Looking through the turn or looking where you want to go is always good advice for any vehicle. When you do that it really makes it easier to ride or drive more smoothly.
Another little example of using counter steering. I ride a lot with clipless pedals. If you search around here you'll find legions of stories about falling when learning to use clipless. A little "trick" I use when coming to a stop is to unclip one side and just before I come to a stop with the last shred of forward motion I push the grip on the side of the loose foot quite strongly. This starts a strong lean into the loose foot which I then place on the ground as I come to a halt. It makes sure I don't have a story to add to the legions of examples...
It's also a strong proof that this counter steering "trick" works at all riding speeds. Again I urge you to go out and work with it in an open lot and really work on using bar pressure to control the steering and balance at all speeds. Yes it's possible to steer a bike with leaning. In fact steering with no hands on the bars is a way of working with both the stabilizing caster in the front end where you sort of alter your balance to make the bike do the counter steering for you. But it's not anywhere near as immediate or accurate as actually pushing the bars yourself.
While it may alienate me with the folks that say they just lean into the turn you can't steer a bike really well by just leaning. Ride a heavier motorcycle and it'll teach you that fact REAL quick. What happens with people that have taught themselves to steer by "leaning" is that they subconciously push forward with their shoulder or elbow on the bar in the direction they lean or somehow twist the bars to achieve the same "push to turn" I described above. That induces the whole counter steering process for them. But since it's not a concious use of bar pressure the brain never quite learns just what action is actually doing the steering. It becomes more a "faith" thing. Now that's fine for those folks and there's many, many good riders that'll tell you that it works and for them it works just fine. It's how we learned to ride as kids. But when you're doing this from scratch you may as well learn to control the bars correctly from the get go. When you learn to steer with bar pressure you'll find that it's easy to lean the bike any way you want but you can still turn the way you want even if it's contrary to how the bike happens to be leaning at the time. For example there's this post in a tight spot that I go around every day. I have to lean the bike slighty to the right while I'm actually turning the bike in a left hand arc with my body hanging way off to the side to keep the bars from hooking the post and dumping me into the dirt on the trailside. I can do this because how I balance the bike to shift it to the side (hanging off) and how I turn it (bar pressure) are separated in my mind rather than being locked together. It's a handy skill at times....