The most common anti-lock braking system problems include a blown fuse to the system. Another common problem may arise from corrosion or damage to the wiring harness for the main controller or to the wheels and sensors that monitor the speed of the car.
Troubleshooting the ABS system should begin at the fuse box, as that is the simplest repair. The owner's manual has a diagram showing which fuses power which systems.
If the fuse isn't the problem, looking at the ABS controller harness for any corrosion is the next step. After that, it's necessary to look at the sensors by each wheel. If one of these is dangling, replacement is likely to be the best option. Toothed wheels next to each axle or wheel-bearing assembly monitor speed, and damage to those wheels also causes problems in the ABS system.