Remove as much snow and ice from the roof as possible using a snow rake or push-broom. Focus on removing snow from a few feet above the ice dam to the roof edge.
Cut drainage paths through the ice dam using a stream of warm or hot water from a hose or faucet. If the roof has a slight enough slope that you can work on it safely, then you could stretch a hose closely to the ice dam from the roof. Place the hose's stream of water as close to the ice as possible, and work upward from the bottom to create a drainage channel. The drainage channel created by this method will last only a few days under most conditions and must be recreated or used in combination with other techniques.
Apply a deicing compound to the roof. Use a compound that will not corrode the roofing material. Place small piles of deicer directly above the ice dam, and then sprinkle a line of deicer across the ice to the roof's edge. Alternatively, fill a nylon stocking with deicing compound, tie off the stocking's open end and then lay it across the ice dam to create a longer-lasting drainage channel.
Lay electric heating cables in loops along the roof's edge or gutter. You may stretch the cables across the roof to cover as much roof as desired. Extend the cable loops slightly beyond the roof edge to allow for drainage.
Implement long-term solutions for the ice dam. Increase the amount of insulation in the ceiling or attic, seal places where warm air can leak through the ceiling or roof and improve ventilation so that cold air can flow under the roofing materials.