Use a tape measure to obtain the length of your roof along the roof peak. Divide the distance in half and make a mark for the location of the cupola.
Take two 1 by 4 pieces of wood and place them flush against the roof peak at the center mark. Ensure that one piece rests against one slope of the roof and the other piece lies on the other slope. Clamp the two boards where they intersect at the top of the roof.
Use a drill to screw the boards together at the exact angle of the pitch of the roof. This give you a template for cutting the cupola to the proper angle.
Mark a straight vertical line with a pencil where the two boards join together. Check for plumb with a level.
Draw a vertical centerline on two opposing sides of the cupola base. Place the 1 by 3 template over the base, ensuring the vertical lines on both surfaces match up. Ensure that the intersection of the 1 by 3s rests near the top of the base.
Draw lines along the inside of the template from the end of the template to the centerline. Repeat the placement of the template and the line markings on the opposing side.
Cut along the marks you made on the base starting at the corners with a circular saw. Discard the excess you have removed from the bottom of the base. Cut four pieces of 2 by 4 lumber to fit alongside the four angled sections of the base.
Place the cupola base at the mark on the roof ridge you made earlier. Place four 2 by 4s on the inside of the cupola, one against each angled side. Use a drill to screw the 2 by 4s to the roof.
Drill two holes on one angled side and fasten the cupola to the 2 by 4s with screws. Repeat for each angled side.
Place the midsection of the cupola on the base. Nail it to the base with a hammer. Set the cupola top over the midsection. Nail it to the midsection.