Place a level on top of your refrigerator to determine if the fridge is level. If it is tilting at all, the unevenness can cause water to pour out of the ice maker. Adjust the feet of the fridge by turning them in or out of the fridge to elevate or lower the edges until the appliance is even.
Check the freezer and the fridge to see if the lights and cooling systems are working. If they aren't, check the breaker. If the freezer is thawing because the power is cut off, the water is due to the ice in the freezer melting. If power isn't the problem, unplug the machine for now while you inspect the ice maker up close.
Break up any ice clusters built up inside the ice maker carefully with an icepick. If the ice is freezing solid, it can impede the machine's function and cause the water to leak out because it can't make it into the reservoir and doesn't have time to freeze.
Unscrew the ice maker from its frame and unhook the wiring harness to get a better look at the ice maker; the specific method for this will vary depending on the model of your fridge, so check your manual. Check the housing, water inlet tube and other hoses in the ice maker for leaks. If a hose is loose or has cracked, seal or replace it to stop the constant flow of water.
Request a professional examination of the ice maker if is still leaking. It may require a full replacement.