Refrigerators are supplied by a water line, which can become clogged for a number of reasons, including ice buildup. The water line is a metal tube along the bottom of the back of the appliance, usually made out of copper, that supplies water to the water dispenser in the door.
Unplug the refrigerator.
Unscrew any connectors holding the water line in place and place a towel on the floor underneath where the water line has been disconnected.
Push the button on the door of the fridge for water. If the water comes from the disconnected water line and spills onto the towel, it is likely that there's a blockage in the pipe between the opening and the door of the refrigerator. Otherwise, the clog is in the portion of the water line going from the wall to the refrigerator.
Replace the connectors.
Push the button in the door continuously if the door line was frozen until water comes out of the dispenser, leaving the refrigerator door open if possible.
Leave the refrigerator unplugged for as long as possible, at least two hours, to allow the ice buildup to thaw if the clog is not coming from the door's water service line.
Plug the refrigerator back into the wall, and try the dispenser after a few hours. The dispenser should be working properly and be unclogged.