Decide on the height and pitch for the roof. Measure and mark the spot for the Dutch gable. Decide how far down from the main roof peak you want it to go. Mark that spot and cut a 2-by-6 ledger board to go between the common rafters on either side to serve as a ledge to attach other rafters. It will be the starting point for the hip slope below the Dutch gable. Nail the ledger board to the outside of the two rafters; make sure it is level.
Cut two Dutch common rafters, to run from the ends of the ledger board to the two corners of the wall. Cut a "birdsmouth" notch where they meet the wall, 1-inch deep and 4 inches long, triangular to fit tightly against the wall cap. Nail those rafters in place.
Cut hip rafters for both sides of the roof, from the Dutch common rafter to the outside walls. They will parallel rafters on the rest of the side roof. Put birdsmouth notches in those. They will vary in length down the roof. Nail them 24 inches apart. Cut the length so any overhang is the same as side rafters on the rest of the roof.
Measure and cut common rafters to run from the Dutch gable ledger board to the outside wall; make birdsmouth notches and allow overhang the same as the side rafters. Space them 24 inches apart. Then cut hip rafters to fill gaps between the last common rafter on each side and the outside wall; these will run from the side common raffer to the end wall. Make birdmouth notches and allow the same overhang.
Put oriented strand board (OSB) decking over all rafters. Cover the Dutch gable with the finish materials of your choice. Nail metal flashing under the siding of the Dutch gable and the top of the OSB. Lay down roofing paper and nail shingles on the hip extension. Finish with a fascia or facing trim board nailed to the ends of all rafters.