Tips for noobs:
Going fast on a circuit is about maximising speed around corners and maintaining momentum as much as possible. Powerslides are fun, as are handbrake turns, but they won't help you get your lap times down. Cornering fast is about stability and smoothness. The smoother you can turn, the less speed you'll lose and the faster you'll come out of the corner.
Every corner has a path around it which will give you the best speed. Actually, there are numerous lines you can take, but they're all pretty close to each other. This is called the racing line; the Forza racing line assist follows these lines reasonably well but the real joy of driving games is working these out on your own and learning when you can break the rules.
The principle is that you want to wait to slow down until the last second, then brake until you're at the right place and speed at which to initiate the corner, release the brake (or 95% of the brake), go around the corner in a smooth fashion whilst cutting the apex and power out of the corner as you start to straighten the wheel.
The basic parts of a simple corner are:
1 - Brake point
2 - Turn in point
3 - Apex
4 - Throttle out
Check out this article:
http://www.drivingfast.net/techniques/racing-line.htm
One last important tip - you MUST pick manual. Don't worry about manual with clutch, just manual is fine. You get the correct speed for each corner by remembering which gear you should be for each corner, not by looking at the speedo. For instance, corner one in Mt Panorama could be taken in a high 2nd gear or a mid 3rd gear, depending on the car. The the next corner may be a high 3rd gear or a mid 4th gear. You simply can't get that with auto. For student race car drivers, they often cover up the speedo. In terms of racing, speedos are useless. You'll often hear race commentators talking about 2nd gear corners, 3rd gear corners, etc.
To reiterate - every corner has an optimal racing line around it. For this line, there is an optimal speed. To pick the right speed, remember which gear you're meant to be in for each corner. Also remember the brake point you use for every corner and every turn in point. As you hit the brake point, brake hard as you can without locking up the wheels and downshift until you get to the correct gear/speed. If you picked the correct brake point, you should be in the right spot and at the right speed to turn into the corner to cut the apex. If you are not, adjust the brake point on the next lap.
Hint - find the next track you're going to race on. Quit to the main menu and set up a single player race with no AI on that track, make it 10 laps. Just keep lapping around with the racing line off on your own. Every lap try and improve your time.
Now when you're doing your laps on your own, try and perfect the four parts of every corner. If you get the technique down, your lap times will improve. It's also fun as hell in a nice car to just lap, trying to beat your best time. You'll get credits for it too and XP.
Once you get good at lapping, you can go back to career mode and then apply your skill at lapping with the added fun of crazy drivatars.
Yeah, I agree with everything, but the bolded point is something really strange. I've bought cars and modded them, only to find out that my car no longer qualifies; at this point I find out the requirements. It's annoying and simple to fix.