Measure up from the ground and mark the pole to the left side of the window installation area at a point 1/2 inch below where the bottom of the window jamb will be installed and 1/2 inch above the top. Use a piece of mason's twine and a string level to stretch across from each mark to the pole on the right side of the installation area and mark the post so that it is level with the marks on the left post.
Measure the distance between the bottom and top marks. Cut a 2 by 4 so that it is 1/2 inch longer than the distance between the poles at each point. Trace a curve that is the same radius as your barn poles using the end of a pole that is the same size as your barn poles. Trace the curve onto the wide face at each end of each 2 by 4 so that it is 1/4 inch in from each end. Cut the curves with a jigsaw.
Fit the 2 by 4's between the poles with the top face of the bottom board even with the mark and the bottom face of the top board even with the mark. Check both boards with a level and adjust as needed to center the bubble in the indicator. Measure the distance between both boards at each post and adjust as needed to make them equal.
Drive two 3-inch treated deck screws up at an angle through each end of each 2 by 4 into the poles, holding them firmly to prevent shifting. Find and mark the center from pole to pole on each board with a tape measure. Measure from this point and mark a distance one-half the width of your window from outside to outside, plus 1/4 inch. Mark a straight line on the two outside marks on the top and bottom boards with a rafter square.
Measure and cut two 2 by 4's to fit between the top and bottom horizontal 2 by 4's. Align one with each of the marks on the horizontal 2 by 4's so that the inside face of the board is aligned with the line. Drive two 3-inch treated deck screws up through the bottom 2 by 4 and down through the top 2 by 4 into the ends of the vertical 2 by 4's.
Drill through the siding to the outside in each corner of the window opening to mark the position of the frame. Draw lines connecting the four corner holes on the outside of the barn siding. Use a circular saw to cut the opening along all four edges. Drive screws through the siding into the 2 by 4 frame, placing two screws on each side of the window opening.