Unplug the refrigerator's power cord. Turn off the water shut off valve for the refrigerator's ice maker, if present. Use an adjustable wrench to loosen the water line from the refrigerator.
Incline the refrigerator carefully to one side. Slide a furniture skid beneath the two refrigerator knobs serving as feet. Lower the refrigerator, then repeat the process for the other side.
Grasp the side of the refrigerator and slide the unit using the skids over the peel and stick tile. The skids with prevent the unit from tearing up the tile as it moves along.