The first step to troubleshooting an anti-lock brake system is checking the fuse that manages the brakes. If the fuse is functional, check the harness of the ABS controller for signs of corrosion. Then check the wheel sensors. If those are in order, you might need a new ABS controller.
Check the owner's manual for the diagram of the fuse box. Locate the fuse controlling the ABS system, and replace it if you see any signs of discoloration or corrosion. If the ABS light on the dashboard hasn't shut off, look at the harness for the controller. Look in your owner's manual or search the Web for your car's controller location. Spray the harness with aerosol contact cleaner, and look for any indicators of corrosion. Then unplug it, and plug it back in.
Each axle or wheel bearing assembly has a toothed wheel with a magnetic sensor next to it. This tells the ABS system how quickly each wheel rotates. Loosen the lug nuts on a tire, and jack the car up after blocking the opposite wheel. Look at the harness and sensor at each wheel. If it is loose or missing, or if the wires show damage, this is likely the problem. Look at the teeth of the tone wheel for damage. Follow the manufacturer's instructions for replacing these items, or take it to a mechanic if you don't feel comfortable working with a braking system.