Understeer - need to brake with the rear wheels to solve the problem. Hanbrake is an emergy solution very effective (must be soft on it). Setting the brake bias with with a x/x+y, being y>0/\10>y is how you should tune your car (oversteers early to allow you to start accelarating early on the exit). More weight at the back, less at front or messing with suspension (stiffer at the rear soft at front). Even putting more weight at front will help. In a AWD you can also increase the torque at the rear wheels instead of using the previous solutions. Using different tires is another solution, but it isn't much of an advantage in racing in gt5, just for fun. Increase downforce at front and take it at the back. Many times you just need to use some of the tecniques, depending on the case when understeer occurs when chosing them.
Oversteer - Voted for this. Yeah its much more fun to balance between throtle and countsteering when the car is sliding. It improves techique that can used when drifting or rallying and is stylish. Although it can waste more tires in an FRcar (in MR and RR there have more weight on the back (relatively), so less oversteering, ceteris paribus). An easy way to avoid is to shift up before the time it starts to oversteer. to tune it: stiffer suspension at the front (not a very good solution in some cases) and making it softer at back, seting more weight at the back also help. More downforce at the back and brake bias stronger to the front. In 4wd you can also set the torque distributer higher to the front. Can also race with different tires but is the same as stated above, IRL you can also decrease tire pressure (see dragcars). Many times you just need to use some of the tecniques, depending on the case when understeer occurs when chosing them.