To build a cupola, make a construction plan including the desired dimensions. Assemble all the necessary tools and building materials including a sliding miter saw, lumber, galvanized screws and shingles. Construct the ventilation house using a frame of posts and cutting coves into three of the corners for an ideal fit. Then install four vents in the frame as the ventilation house walls. Cut and fit curved rafters, then add roofing sheathing to build a witch's cap-style roof.
Use the sliding miter saw to cut the frame of the ventilation house. If a sliding miter saw is unavailable, use a circular saw. When fitting and securing the vents onto the ventilation house, use duct tape to hold them in place while drilling the galvanized screws. There may be cracks between the vents and the frame, so fill these with caulk to seal the ventilation house. Finish the wood aspects of the ventilation house with veneer or sealant and paint as desired.
Cut and curve the rafters with a jigsaw. If a jigsaw is unavailable, use a circular saw. Mark the curves of the rafters so the curve matches on all rafters. Cut and mount roofing sheathing over the rafters, taking care to trim away any excess sheathing. Finish the witch's cap with shingles.
After constructing the cupola, use a simple cross saddle to mount it over the roof's cupola hole. Build a frame of railing to fit the cupola onto the saddle. Secure the cupola to the frame with galvanized screws, caulk and roofing cement.