The physics of driving into and out of a curve or turn

Any of you racing enthusiasts, I am a driving instructor trying to write a page on driving on curves and winding roads.
I want to explain a little of the "physics" of why the smoothest way through a curve is to brake before the curve, coast in the curve and gas out of the curve.
I know braking transfers weight to the front of the vehicle, pushing the gas pedal transfers weight to the back, plus lateral weight transfer to one side or the other in a curve.

How do these laws of physics and friction work together to make braking before, coasting through, gassing out, the smoothest method for average driving?
(explained in laymens terms, so the average driver could understand it.)

Any input is appreciated!

CL8