How do I prevent ice dams from forming on the eaves of an addition?
The way to prevent ice damning is to prevent the snow on the roof from melting in the first place and that means adequate insulation and venting in the attic. If the insulation of your home is not adequate then warm air from the living space fills your attic and melts the snow on the roof, the melted water then run down the roof where it freezes over the eves because the eves are not warmed from below.

Ice-and-water barrier or heat cables do not address the reason for the ice damning in the first place. Ice-and-water barrier will minimize damage that can be caused by the ice and the heat cable can melt the ice ( or prevent it from becoming so thick it does cause damage. 

You have to prevent the melting, anything else does not fix the problem.