This is kind of repeating what the others have said, but what the heck. Two things go hand in hand to make for the fastest laps.
- Proper gas and brake modulation. Don't have a heavy foot. Press the pedals as gradually as you can, especially accelerating through turns.
- Steer as gently as possible, meaning, work to make your turns using the least wheel/controller movement you can. Straighter wheels mean more grip and faster speeds.
Also, learn to coordinate your acceleration with your turning. Giving either car a lot of gas when your wheels are cranked will just get you spun out. As I said, you can give it more gas the straighter your wheels are. You can also give it more gas in a higher gear, such as 3rd instead of 2nd. But you should just use this to get your racing line down, and then focus on having your car in the proper gear. You'll accelerate slightly faster, and shave tenths of a second off your time.
Finally, learn to drive in manual transmission mode, and if you use traction control, wean yourself off of it. This will probably be one of the biggest time savers for you.
This is common knowledge to the PC sim racers, but then, this is very much like a PC sim now, so you have to unlearn all your bad console racing habits and treat this thing like a real car.