The main cornering mistake most riders make is not using their eyes. Instead of looking at the turn carefully, well in advance of approaching it, they stare too near their front wheel.
Scanning the turn early helps you choose the correct speed and best line. Then:
Approach the turn as wide as traffic and other conditions allow.
Cut through the turn on nearly a straight line.
Exit wide, again using as much of the road as you can safely inhabit.
Keep an eye out for potholes, gravel, oil slicks, and errant pedestrians. These obstacles are easy to avoid by adjusting your line slightly. But you can do so safely only if you see them well in advance.
Whenever you ride, and especially when coming to a turn, remember the advice of your old linebacker coach: "Keep your head on a swivel!"