How do you check to see if water pump leaks?

Most water pumps have a small vent hole on the bottom side of the pump. Inspect with a flashlight and check for staining (rust or color changes left behind after water runs away from the vent) related directly with that vent hole. Also check for play (side to side) in the input shaft (belt pulley or fan pulley Either of these conditions is an indication of a failed or failing water pump.