drive and drive and drive ... practise practise practise.
learn the tracks, the line, the braking, behavior of car under braking, accelerating, cornering (the basics of physics in game) and just get all gold licenses. If you do that, you will learn how to drive fast.
Practice racing lines, even if it means you slow down, you'll get used to it and get faster again, finding you go faster than you used to, use analogue sticks for acceleration and braking and steering.
Use Manual gears.
When cornering - go slow in and fast out, especiall if you have a longer straight after the corner. Brake earlier into the corner in order to get higher top speed on that straight. And main point - be as smooth as you can be.