Using a saw, cut a slit at each end of your 12-inch length of wood centered along its 2-inch side about half an inch deep. These slits will be where you insert and arrow head and pointer of the weather vane.
Measure 6 inches in from one end of the wood, and tap a nail through the mid-point of the 1 inch side of the wood until the tip emerges out the other side.
Stand the dowel vertically and place the metal washer on the top. Line up the tip of the nail with the center of the washer and hammer the nail down into the dowel, connecting the two pieces of wood. Rotate the 12-inch piece of wood on its axis a few times to make sure it spins easily.
Cut an arrow head and tail from the metal pie plate. These can be any size you choose, but they must be large enough to catch the wind. Fix the arrow head and tail into the slits at the end of the 12-inch piece of wood using glue.
Mount your completed weather vane to the roof of your house, using wire. Make sure to wrap the wire around something solid, for example a chimney or guttering.