Climb into your attic, and locate the area of roof that is leaking. The leak may not be originating exactly above where the water is collecting on your ceiling, so investigate the attic with a flashlight and look for water damage and a trail of dampness that leads to the leak.
Place a box fan in your attic, pointing the flow of air at the location on the roof where the water is leaking. Turn the fan on the highest setting, allowing it to circulate the cold air onto the roof around the leak and freeze the water.
Stand on the ground, at least five feet away from your house, and place a roof rake on the roof with the wheels pointed down. Drag the rake from above the area of the ice dam all the way off the edge of the roof repeatedly, pulling the snow off the roof.