Constructing the roof of the cupola can be the most time-consuming part of the building process. Part of this is because most cupolas for the home feature a curved roof. Cutting and assembling those curved rafters is tricky. To make the process go smoothly, use a jigsaw, and don't worry too much about making the curves perfect. Make a roof sheathing to cover over any bumps or irregularities.
The most important part of constructing a cupola is ensuring it fits against the angles of the roof. An easy way to cut the correct roof slope on the bottom of the cupola frame uses only a pencil, a level and a sheet of cardboard that's one foot longer than the base of your cupola.
Go up to the roof and position the cardboard at the ridge of the roof, using the level to make sure the edge is straight. The top of the cardboard should be about three inches higher than the peak of the roof. Reach around the cardboard and trace the roof line on the back side of the cardboard. Then, cut away the top portion of the cardboard with a razor blade, and use the cardboard as a template to measure the roof angle against the base of the cupola.
If you want your cupola to provide ventilation, you'll have to cut a hole in your roof when you install the cupola. Make sure you do this the right way. Be careful to cut only through your roof's sheathing and not into any of the structural lumber underneath. Use an old saw blade, not a new one, to cut through the shingles. Cutting through asphalt shingles will ruin a good saw blade.