Stay off the brakes as the brake pedal behaves like a handbrake. The slightest steering while braking for a corner will send you into a permanent snap spin. Lift off the gas to start the auto-braking feature and your car will slow down sufficiently for almost every corner in the game.
Even with the Rules Enforcement option turned on you can use shortcuts at many of the chicanes at most tracks. You will have to determine how far off the track your car can go without incurring a "shortcut" penalty by trial and error.