I'm not big on this game. Got it free with my Radeon 4870. It looks awesome by the way. But I have played it a bit, mostly to show my family how far graphics have come since the Super Nintendo.
Its like most other racing games. Dont kill yourself trying to get first place right way.
Just drive well and slowly overtake them by the last lap.
If you cant drive well its all pointless. Try some practice runs by yourself. When you get talented enought that you can go around the track a few times without making any mistakes then your driving skills are good enough.
Go into some competitive modes and use your skills against the other drivers.
The first modern race game I played was Test Drive Unlimited. And because I hadnt played any console titles in years and never played a race game on my computer it kicked my butt for a while.
After lots of practice I got into it and eventually got pretty damn good.
Same thing with GRID. First few rounds I was pushing into the wall half of the time.
Eventually I got better. But only with PRACTICE, PRACTICE, PRACTICE!
There are no real tricks, you just need skill. And skill comes from playing the game alot.
Out of curiosity, what kind of controller are you using?