An ice dam forms when heat escaping from the attic melts snow on the upper part of the roof. That water runs down to the cold eaves, refreezes, and builds a ridge of ice. The next round of meltwater pools behind the ridge and works its way under the shingles, which is how a perfectly good roof ends up leaking in February.
In Orleans, Niagara, and Genesee counties, lake-effect snow and constant freeze-thaw swings make ice dams more common than almost anywhere else in the state. Older farmhouses with little attic insulation are especially prone to them.
The best prevention starts before the snow. Clean gutters let meltwater drain off instead of backing up. A roof checkup in the fall catches lifted shingles and failed flashing where water would get in. Good attic ventilation keeps the roof deck cold and evenly frozen.
Once snow is on the roof, clearing the lower three to four feet after a heavy storm takes away the fuel for a dam. Use a roof rake from the ground, or have a crew do it. Never chip at ice with a hammer or shovel, which damages shingles faster than the ice does.