Reach behind the washer and find the cold water inlet tube. You may need to pull the washer away from the wall to get to the tube.
Trace the tube back up to the cold water line valve. Turn the valve to the open position. Attempt to run the washer on a cold water cycle.
If the cold water doesn't start pumping, turn off the washer and unplug it. Locate the water inlet valve on the back of the washer. This is the unit that the hot and cold water lines run into.
Turn off both the hot and cold water valves. Open the inlet valve housing. Depending on the washer make and model, you may need to unscrew screws to open the housing. Disconnect the cold water tube.
Inspect the screen inside the water line or in the inlet valve housing. If the screen is clogged, rinse it under warm water before putting it back in place. If the screen is already clean but you still have no cold water, the inlet valve is defective.
Remove both water lines from the inlet valve. The water should still be off. Unscrew the valve housing from the wall mount or back of the washer. Install a new one that matches the old valve. Reconnect the water lines and turn the water back on.