If your vehicle has a faulty anti-lock braking system module, replace the module, and then bleed the brake system. You need a VAG-COM diagnostic tool, a hydraulic pump, star screwdrivers, line wrenches and box wrenches. You also need 3 liters of brake fluid and a brake bleeding kit.
Use the VAG-COM diagnostic tool on the faulty ABS module, and write down the code it displays. Wait for the engine to cool, and lift the car on four jack stands. Remove the cable from the negative terminal on the battery, and then remove the positive cable. Remove the battery altogether.
Place a bucket or pan underneath the bleeder screw on the brake reservoir. Remove the bleeder screw, and allow the fluid to drain. Lay a shop towel underneath the brake master cylinder.
Use the line wrenches to remove the lines connected to the module. Pull the T-shaped handle on the module toward the front of the car, and move the wiring harness. Use the star screwdrivers to remove the brass bolts on the modules. Coax the unit out of the vehicle gently, and be sure to avoid damaging the brake lines. Remove the hydraulic pump as well if necessary.
Install the new module and hydraulic pump, and bleed the brake system. Return the battery. Use the VAG-COM tool on the new module to ensure the code matches the faulty one. Code the module manually if needed. Use the VAG-COM software to cycle the new hydraulic pump.