If you have an internet connection, I suggest you take advantage of the download function in Arcade Time Trial mode and download the fastest guy you can find, then watch his replays and how he does it.
When I'm driving for fun, I hit the brakes, line the car up while cadence braking, then pitch it sideways for a slightly drifting line. Then get on the power as soon as the car can take it.
If you want the proper line, you brake hard, turn in and nail the apex, no matter how slowly you have to go to do it, and take a very neat and straight line out.