There are three ways to turn a corner on a motorbike and the method you use depends on your speed and how tight you want to turn.
Using only the handlebars
At speeds below 10-15km/h steering is mostly accomplished by turning the handlebars to initiate the turn, then adjusting your weight to maintain your balance. There’s very little centrifugal force and therefore no need to tip the bike over much in the corners. At less than walking speed, it requires excellent balance to stop the bike from tipping over when turning.
At speeds above around 10-15km/h, you hardly move the handlebars to turn a motorbike, unless you need to turn extremely sharply. It’s mostly done using countersteering. Countersteering is an almost subconscious procedure that balances the rider’s angle in the corner with the centrifugal force and the desired turning angle. Basically, cornering is like you’re falling off the bike sideways but you’re correcting your line to use centrifugal forces to keep the bike from tipping over completely.
How does this work? When you’re turning in a car, you simply turn the steering wheel in the direction you want to go. It doesn’t work like that on a motorbike. To initiate a turn on a motorbike you actually very briefly turn in the opposite direction.
Let’s say you are approaching a right-hand bend. To initiate the right-hand turn, you push forward on the right-hand handlebar. This tips the motorbike to the right. You then turn the handlebars very slightly right (the bike does this automatically) and lean in with the bike. This creates the radius of the curve. To return to an upright position, slightly pushing the left handlebar will tighten the turning radius, increasing the centrifugal force, meaning the bike will stand up (unless you deliberately lean into the corner more).
Once the bike is moving, it has kinetic energy forwards and the wheels have gyroscopic energy. Both want to remain moving in the same direction (straight ahead) as long as the weight is balanced. You can make slight turns just by shifting your weight. If you remove your hands from the handlebars and shift your position you’ll see that the bike will follow your weight shift. As the bike leans slightly, the handlebars will turn automatically to the plane of least resistance. This is assisted by the steering geometry setup of the bike. You cannot make sharp turns like this.
If you lean the bike and keep the handlebars straight, then you’ll remain in a straight line; you may have to do this in a strong side wind.