All motorcycles, and the tires fitted, have a finite amount of grip. Cornering at an advanced level requires a well set up bike, with good tires fitted, and a rider who is aware of his and the bike's limitations (not all bikes can corner like a MotoGP bike). If the bike is a classic racer, it will be capable of cornering at a greater lean angle than a street bike.
A race bike will have much more clearance around items such as exhaust pipes and foot rests when the bike is leaned over to its maximum.
Although learning to corner at an advanced level will go hand-in-hand with advanced braking, a rider can get used to cornering faster on long corners easier than short ones. Riders in the UK will find that the Gerard's bend on the Mallory Park circuit is an ideal corner to gradually increase both speed and, by extension, lean angles.
In the US, Roebling Road Raceway near to Savannah in Georgia has a similar bend leading onto the start finish straight.
On long bends such as those mentioned, the rider will enter the corner at a speed that he feels comfortable with, but some way off the maximum possible, then gradually open the throttle increasing the lean angle proportionally.
If the rider feels that he is beginning to go too fast or the lean angle is becoming too much, he should simply close the throttle. However, this closing of the throttle should be done gradually so as not to upset the balance of the bike.