I'm not that good in racing games either, but I slow-down before the turn, then when I'm turning I hit brake at right times(basically I release-press-release-press..) and I sort of drift-drive through it. Dunno if this is such a good technique, but I've won races with it so I'm sticking to it.

UPRC, I didn't get the chance to say this before, but love your avatar and sig. 

Yeah, I just got PS3 too, so bring on the Gran Turismo!!

Haha well it's nice to know I'm not the only one who can't play this type of game. Forza 2 came with my XBox 360 as well. I basically just played it one time ran into every wall on the track & just quit & went back to Burnout. No matter what I did it would always end with me against a wall, like driving on ice. But still it seems like I'd probably like it though because of all the customization options I believe it has if only I could just stay on the damn track.

EDIT: Whoa! Orange00's method works! I mean I'm still ocassionally going off the road mainly because I'm use to flooring it 95% of the time especially in straight a ways & driving aggressively (smashin' foo's), my main racing game experience comes from Burnout & Mario Kart so yeah... but it's definitely working.

EDIT2: ARRGH!!! Screw this game!!!

If I remember rightly, the game actually tells you that you can't easily slam on the anchors and expect the car to turn, just like how blazing around corners will see you kissing a wall.
I've not played it in a while (I've played both versions), but one of the better cars for me was the Dodge Viper models as they cornered fairly well for me and they are fast (as opposed to the usual "I'm going at a billion miles an hour, but I CAN'T FUCKING TURN!!" Viper in some other games).
Once you get onto stuff like the endurance races, you're going to either hate this game or you'll be good at it as there's races with 35 or so laps (or less than 10 if it's Nürburgring, which isn't as hellish as it appears) and if you're good at getting ahead, you can open huge leads.
Another tip is that sometimes, you can turn easier if you come off the gas (braking if needed), turn in and then put your foot down.
All the cars handle differently, so it's a good idea to find a car that drives how you want it to within the requirements of the race.
Don't go over the top with custom bodywork as these will change how the car handles, and they can seriously damage your top speed \ acceleration without giving much back.
Avoid cars like the Corvettes - especially the higher powered ones - or you'll just end up going backwards into a wall or another car.
The Nissan speed circuit is easy money, especially if you can win the Yellow Hat Supra as it's just a big, if slightly deformed, ring.