Things You'll Need
Treated deck screws
Odd-sized or odd-shaped windows always present an interesting challenge. One of the keys to remember is that no matter how you travel around a geometric shape, the total of all angles will equal 360 degrees, or a complete circle. Simply divide 360 by the number of corners to determine the angle of each corner. Divide this by two to determine the end miter for the pieces that make up the corner. With this little trick and some careful measurement, your window will be framed in no time.
Measure the width of the octagon from outside to outside. Measure the height as well, if all sides of the octagon are not equal in length. Cut the drywall from the wall from floor to ceiling in an area 1 foot wider than your window. Remove the drywall to reveal the wall frame. Cut any studs that run through the window's proposed location 3 1/4 inches below the bottom position of the window and 3 1/4 inches above with a reciprocating saw. Remove the cut piece.
Cut two 2-by-4s to fit horizontally between the two studs on either side of the space the window will be framed in. Position one of the them with its top face at the height of the window's bottom edge, minus 1 3/4 inches, on top of any stud you cut in the previous step. This is the frame sill. Place it between the studs, using a level to check and adjust the pitch. Nail through the studs on the sides into the ends of the 2-by-4. Install the second 2-by-4, parallel to and above the first, a distance equal to the height of the window, plus 3 1/2-inches. This is the frame header.
Cut two pieces of 2-by-4 to fit vertically between the two you just installed. Mark the center of the frame sill and header horizontally. Measure from this center mark to either side a distance equal to half the width of the window, plus 1 3/4 inches. Install the two vertical 2-by-4s with their inside faces on these lines at top and bottom, with the narrow edges of the 2-by-4s even with the faces of the sill and header. Nail up through the sill and down through the header to anchor the pieces in place.
Measure each outside edge of the octagon, and cut one piece of 2-by-4, 1/4 inch longer than each edge, with both ends mitered at 22 ½ degrees to form eight 45-degree corners. Make the miters angled toward each other, so that one wide face of the 2-by-4 is beveled to 1 1/2 inches shorter than the other. This inside short face needs to be 1/4 inch longer than the face it fits.
Glue and nail these pieces together with wood glue and a pin nail gun with 2-inch nails, three per joint. Add pieces until the octagon frame is complete. Drill two 1/8-inch diameter pilot holes in each joint, and drive two 1 5/8-inch treated deck screws into each joint to reinforce it. Set the octagon frame into the frame you made with the 2-by-4s. Nail this frame in place, driving the nails through the 2-by-4s you installed into the octagon frame on all four sides.
Drill through the wall with a 1/4-inch bit at each inside corner of the octagon, through the sheathing and siding to mark the exact position of the window on the outside wall. Draw lines to connect these holes with a marker on the outside of the wall. Cut this octagon from the wall with a circular saw to create the window opening. This completes the frame for your octagon window.