I wrote this in the Nighthawk Forum for a new-to-the-street former dirt-bike rider:
A bike turns by leaning, which means the center of gravity (both of the bike and the rider combined) is no longer directly over the tire contact patches. However, the bike does not flop left or right over the tires; instead, the bike rolls around the center of gravity, approximately where the top of the engine is. The tires move to one side while the rider moves to the other side.
What controls a bike's pathway around a turn are the speed and the angle of the center of gravity relative to the tires' contact. You can't change the radius of the curve, so you have to control the lean. The greater the lean, the faster you can take a given turn. Some curves change radius, so you have to be able to change your lean angle mid-turn. This is where counter-steering comes in.
Years ago, the Honda ELF racing team tried moving the fuel tank under the engine, to lower the center of gravity, but the riders hated it. The bike handled worse, not better. The bike tried to pivot around the center of gravity, where the main mass was located, but it was unnaturally low, and affected cornering negatively. The next season, they moved it back up and everyone was happy.
On the street, counter-steering is control. Counter-steering is controlling the lean by applying twisting pressure to the handlebars, which steers the front tire out from under the center of gravity to initiate a turn, and then back under the center of gravity to straighten out. You can also adjust the turning of the bike in the middle of a turn, changing the turn radius and staying in your lane.
A bike can not be ridden without counter-steering, but many riders don't realize they're doing it. They believe they turn by leaning themselves and the bike, and the steering just follows. If you consciously steer the handlebars, you have much more control. You can control the lean of the bike independently of your body, and change turn angle and direction much more quickly.
If you watch road racing, especially through the S-curves, you'll notice the bikes flip-flop side-to-side at a rate that is impossible to do without counter-steering. When the racers hang off on the inside of a turn, the bike wants to turn more sharply, because the center of gravity is farther away from the tire contact patches. They're actually using counter-steering to reduce the turn angle.
They hang off so the center of gravity is farther away from the contact patches, so they can take the turn faster, but the bike itself is able to lean less than it otherwise would if they sat at the same angle of lean as the bike. This is done so the bike's hard parts don't contact the pavement and lever the tires off the pavement, which would reduce traction and cause the bike to slide off the track.
There are a few things you can do to maximize your riding skills. Make sure your tires are in good condition and properly inflated. Take your time and learn both your limits and the bike's limits. Pay attention to the condition of the road you're riding, especially gravel, grit, grass, water, oil, etc. Make sure you're not too tired, hungry, angry, or distracted to ride safely.
As mentioned above, you will ride the bike in whatever direction you're looking, so look far around the curve with your head and eyes horizontal, not leaned over with the bike and your body. If you look off the road, expect to go there. Also, find an empty parking lot and practice slow maneuvering. Work on slow starts, turning from a stop, U-turns, figure-8's, panic-braking, etc.
It takes years of experience to become a proficient rider, so be easy on yourself. I have been riding for over 45 years, and I'm still learning. I have been riding my NH750 for years, and riding it is almost 100% instinctive. I just recently got an ST1100, and I ride it almost like a beginner, almost starting over. I have to learn its handling characteristics just like I did those of the NH.
In tighter and/or higher-speed curves, it's good to brake and downshift before you enter the turn, so you finish slowing by the time you're in the turn, and you should actually be accelerating through the turn. You should be in a low-enough gear that you can use the throttle to control your speed, whether accelerating or slowing using engine braking, and not the brakes.
Not a crazy amount of engine RPM, but in the 3000 to 5000 RPM range, depending on your speed and the curve. Just as the brakes shift weight onto the front wheel (which is why the front is a disc, and you should practice and learn how to brake hard with it), accelerating shifts more weight onto the rear wheel, increasing its traction and improving handling and control.