I play all sorts of driving games. From Nascar 08 to Neeed for speed: Pro street. In my years of video game racing experience I have learned a lot of things. I do not claim to know it all. Now I am not a professional driver, and I don't own a fast car, but I belive in my abilities and knowledge that has developed.
I think the main thing you need to learn is NOT TO OVER DRIVE THE CAR!!
Anyone that has experience with racing games will tell you this. Fast is not always fastest. What I mean by that is when coming into the corners don't drive the car in so fast that you mess up your line. Ease the car into the corner and you will see results in your laps times! Find the right line for the striaght-away speed you carry and apply the least amount of brake possible to slow the car down. If you sail the car in the corner you will most likely brake too much and kill your center speeds.
There are three methods I know of when going thru a corner.
Stay on the imaginary white line at the edge of the pavement going around the turn..Hug the corner.
You can diamond the corner. Which is self explainatory, you drive the corner in a diamond. The hope is to get better drive off speeds. It just depends on the corner you are in.
You can drift the corner.
They all have there benefits, but you have the figure out which one works the best on each corner.
Lastly like the others say take the slip control and ABS off and you will take a lot of time off your laps. It may be hard that first, but trust me when you can control the car with those off, you will drive faster.
When I first started to play the DEMO those settings on and I couldn't go any faster than 1.20 average per car. When I turned them off my laps went from 1,20 to 1,15 easily. I have 4 cars where I got 1,10 as my fastest laps now.
Good luck and ease the car in the corners.