One of the bigger adjustments for me was the sluggish steering response with the DS2's joystick -- having been accustomed to GT4's touchy steering, it took a while to get used to Enthusia's. Konami could have made it more responsive and intuitive, but I do appreciate the precision that its slow speed offers.
That said, if you're using the controller, try turning in earlier as you approach corners, and be confident with your steering input. If you start losing it with a RWD car, let go of the throttle, straighten it out before trying to get back into the race, and take that corner a bit slower on the next lap. If you don't feel comfortable with the RWD cars, take one of the several AWD performance cars available.
You could also go to the Airport Square and practice drifting the cars around. Even if you don't like drifting, it's good to know how to keep things under control if you end up sideways during a race. Unless you have a wheel, understeer is only a problem of entering a corner too fast or driving a FWD/AWD car too hard, so if you're plowing off the outside of the corner, then brake more or accelerate less. Enthusia doesn't have the best sense of speed, so you may be flying into corners faster than you think.