Measure the width of the window you want to use and add 1 foot. The result is the provisional width of the faux dormer installation. Measure the height of the window.
Climb onto the roof of your garage in the approximate location you want for the dormer. Locate roof beams that are at least as far apart as the installation width that you calculated, and in the location that you want your dormer to go. The distance between the beams is the final width of the faux dormer installation.
Add 1 foot to the height of the window. This is the height of the installation at the lower part of its roof.
Take a picture of the garage. Lay the protractor down on top of the picture to measure the angle of the garage roof's slope.
Cut four lengths of 2-by-4 that are each equal to the lower height of the dormer installation. Lay one of these lengths flat. Using the protractor, make a line running from one corner of one end of it to the opposite side, at the same angle as your garage roof's slope. Cut the piece along this line. Cut the other three pieces in the same manner. You now have four pieces with one flat end and one slanted end.
Cut two lengths of 2-by-4 that are each as long as the width of the dormer installation. Screw one to the flat tops of the four pieces you just cut. Screw the other to the slanted bottoms. Make sure that the gap between the middle two is exactly as wide as the window that you want to use.
Cut two lengths of 2-by-4 that are as long as the window is wide. Screw them between the middle two vertical lengths of wood in the frame, placing them as far apart as the window is tall.
Place the frame that you have built, which is the front of the dormer installation, onto the location on the garage roof that you have selected for it. Screw it to the roof beams.
Measure the distance from the top of the frame straight back to the garage roof. Cut two lengths of 2-by-4 that are equal to this distance. Set them on the top of the frame, one on each side. Screw those ends to the frame. Screw the other end to the roof beams of the garage.
Divide the width of the dormer installation by two. Square the result. Multiply that number by two. Take the square root of the result. Cut four sections of 2-by-4 to this length. Cut the ends of each of these lengths at 45-degree angles, so that each is shaped like a long trapezoid. Screw two of them to the top of the frame at the front, so that they make a triangle. Screw the other two to the back of the frame, on the long horizontal pieces. These form the frame for the roof.
Install the window into the space on the front of the frame that you built for it. Follow the manufacturer's instructions for installing the window.
Measure the sides and roof of the installation. Cut plywood pieces to fit these areas. Nail the plywood to the frame with small finishing nails.
Cover the sides of the dormer installation with siding that matches your garage's siding. Cover the roof with shingles that match your garage's roof, using roofing nails.