Measure five pieces of MDF 48-by-4.5-inches with a tape measure. Mark the measurements. Measure two pieces of MDF 4.5-inches square. Cut the pieces with a circular saw.
Measure and cut four veneer pieces to match the longer MDF pieces. Measure and cut a square piece of veneer matching the square pieces. Use a veneer saw to make these cuts.
Line up two long pieces with their sides and ends flush. Apply wood glue in an S pattern to one side of two pieces. Sandwich the three pieces with the glue between them touching all three pieces. Keep the sides and ends flush.
Hammer a 1.25-inch finishing nail through the sides of an exterior board through the remaining two boards. This is the core of the post.
Line up a long piece against the each wide face of an exterior core piece. Apply the glue on this piece as you did with the core pieces. Nail this piece to the core face with the same size finishing nails.
Line up a long piece against the narrow face of the core pieces. Apply glue and nail this piece to the core as you did the others. Repeat this step for the fourth side to complete the exterior sides of the bed post.
Apply glue to the edges of the wide face of a square piece. Apply the glued side of the square piece to the top of the post. Make the edges flush. Hammer finishing nails into each corner and the middle of each side on the top piece.
Flip the post over. Repeat the process for attaching the square piece to this end.
Fill wood putty over nail heads and holes with a putty knife. Sand all surfaces with 220-grit sandpaper. Repeat the sanding with 120-grit sandpaper.
Coat the sides and one end of the MDF with glue. Line up your veneer pieces with the sides and top end of the post. Make your edges flush. Rub along the length of the veneer, pushing against the veneer to adhere to the frame and release air bubbles.