Base the size and number of roof cupolas on the length of the roof. Use a simple formula of 1 1/2 inches for every foot of unbroken roof line; if a roof is 24 feet long, for instance, a cupola should be 24 inches square, not counting the slope of the cupola roof. Use two smaller cupolas for longer roofs, basing the size of each on the unbroken roof line surrounding each one.
Buy a ready-made cupola, available from various sources in either wood or vinyl, or make your own. Build a cupola by creating a wooden box for a base to fit over the roof peak, framing vents on its sides and making a roof from triangular pieces of plywood to be covered by shingles. Form the base of either type to the pitch of the roof.
Determine the pitch for a cupola by climbing to the roof peak with two 3-foot long pieces of 1-by-4-inch lumber fastened in the center with a single screw installed with a screw gun. Lay them over the peak, with each board's 1-inch edge flat against the roof slope. Mark the center and secure the boards in that position with a second screw.
Lay a framing square on one angled side of that marker, with the 12-inch mark on the square's thin tongue on the outside edge of the board. Look up the inch mark down the square's wide blade where it touches the top of the board; if that is 7 inches, the roof is a 7/12, rising 7 inches per foot. Use this pitch when ordering or making a frame to fit the peak. Use the angled wood as a jig to cut end-base pieces if building your own cupola.
Set the base of the cupola in position on the roof cap; cupolas typically come in, or are made in, three sections: a base, four sides and a roof. Mark the ridge cap shingles on either side of the base. Remove cap shingles inside and a couple of shingles outside that base area. Pull cap shingles loose with a pry bar, or cut them with a utility knife. Leave the basic roof shingles intact.
Cut the roof if the cupola is for ventilation. Cut a circular or rectangular hole 6 inches smaller than the width of the cupola with a jigsaw; cut between trusses or cut two holes, one on each side, if the roof is framed with rafters and a center ridge board. Do not cut any ridge board or rafters. Install metal flashing across the peak if none is present.
Secure the base to the roof with galvanized screws long enough to penetrate the base and into the roof decking. Put a bead of roofing cement or caulk under the base before fastening it. Follow installation directions with a pre-built cupola. Secure a homemade one by putting 2-by-2-inch cleats on the bottoms of each side of the angled base boards and driving screws through the cleats into the decking. Caulk both inside and outside the base, where it sits on the shingles.
Install the square-vented portion of the cupola and fasten it to the base with galvanized screws. Put the roof on the cupola and screw it in place to the square frame. Shingle the cupola roof if it's home-built; a purchased cupola will come with roofing. Re-install cap shingles to butt up against the edge of the cupola frame. Add a weather vane on top as an option.