I'll give you a bit of advice from the great Jackie Stuart:
Drive smoothly. Imagine there's a big bowl attached to the hood of your car. In that bowl is a tennis ball, which represents the traction your car has. If you yank the car around, the ball will fly right out of the bowl and the car will slide. But if you make your control inputs smoothly, you can work the ball way up onto the side of the bowl, and use all the traction you have available.
I will almost guarantee that you are braking too late. I still do, and so do many people. Try braking earlier so that you are back on the gas immediately after turning in.
Like RER says, watch the demos. In the Replay Options screen, turn on the steering and throttle/brake indicators so you can see what the demo driver is doing as you watch it.
Last but not least: practice, practice, practice.
