If the computer senses that the car is doing something that doesn't match - say one or two wheels are spinning too fast or the car isn't following the curve it should - the computer sends commands to actuators (basically tiny motors) that handle brakes, the throttle and possibly even steering mechanisms.
For now, all these computers do is make sure the car is doing what the driver is telling it to do. Ultimately, preventing a crash is still the driver's responsibility.