Measure out 1/4 cup of mung beans and spread them on a plate. Pick through the beans to remove any rocks and broken or withered beans. Place the beans into a strainer or colander and rinse them well.
Pour the rinsed seeds into a canning jar. Add water to the jar until the water is about 2 inches above the top level of beans. Allow the beans to soak overnight or for 12 hours.
Cut a square of cheesecloth that covers the jar opening with about 2 inches of overhang on all sides. Cut one more square the same exact size. Cover the opening in the jar with the double layer of cheesecloth and secure it in place with a rubber band.
Turn the jar upside down over a sink to drain out the water. Shake the jar to remove as much water as you can. Fill the jar halfway with water through the cheesecloth. Swirl the water and beans around in the jar, then turn the jar over and strain out as much water as you can.
Set the jar upside down at an angle with the bottom edge resting in a small baking dish or plastic container. Lean the bottom of the jar up against a wall to hold it in place. This will allow the water to continue to drain out of the jar, leaving the beans only slightly moist.
Rinse and drain the beans again in the evening, and every 12 hours after that for about 4 days. When your beans have sprouts that measure about 2 inches long, your bean sprouts are ready to eat. Give them a final rinse, drain them off and add them to your meal.