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Glue and screw together the two 12" x 9" x 3/4" pieces of plywood (Image 1); do the same with the two strips of 8 1/2" x 1 1/2" x 3/4" plywood. Center the strips on one of the 9" edges of the plywood base. Screw the strips into place, using a framing square to ensure that the strips are perfectly parallel to the base (Image 2).
Glue and screw together the triangles of plywood. Place the triangle so that its 9" side is flush against the strips of plywood. The point of the 45-degree angle on the triangle should be slightly jutting out on the right side of the base.
With the triangle in position on the base, drill a 1/2" hole through the upper left corner of the triangle and into the base (Image 1). Drill another 1/2" hole in the same position on the upper-right corner of the base. Run the 1/2" dowel through one of the holes and into the base (Image 2).
The triangle can now be flipped 180 degrees, and the dowel will fit into the second hole in the base. This enables the jig to be used for miter cuts in either direction.
Clamp the shooting board to a work surface. Lay a hand planer on its side and take a shaving off the right edge of the shooting board, creating a square end to the 45-degree angle of the triangle. Dust the edge, and finish it with oil and wax to make it smooth.
To use the shooting board, hold a work piece against the exposed edge of the triangle, with the edge to be cut hanging off slightly from the waxed edge of the shooting board (Image 1). Grasp the planer firmly in your other hand. Holding the planer's base tightly against the waxed edge of the shooting board, make multiple passes so that the planer cuts into the work piece (Image 2).