Make a paper pattern for the side pieces.
Clamp 2 pieces of plywood together with paper pattern for side piece attached with repositionable spray glue
Cut out side pieces using a jig saw, scroll saw or band saw
Cut 1 x 4s to desired coat rack length. Mine is 40" long. Cut two more 1 x 4s to that length minus 1-1/2". These two pieces will be the bottom piece of the coat rack/shelf. (Alternatively you could use a piece of thin playwood cut to size: 38-1/2" x 7')
Assemble and attach (using glue and brad nailer) the front, sides and bottom of coat rack/shelf. Sand smooth.
Make a cleat for hanging with a length of 1 x 4 cut to 2" less than the length of the coat rack/shelf. I cut mine to 30". Use table with blade angled to make the cleat.
Now it's time to make the back of the shelf. Cut 11 1 x 4's to 11" long. Line up, edges even, and glue together. Attach one half of the cleat to the assembled back with brad nailer. Attach a second scrap piece of a 1 x 4 approximately 8" away from the cleat. (This will ensure that the coat rack/shelf will hang correctly on the wall)
Now is a good time to paint, stencil, or stain (or all three) the pieces of the coat rack/shelf. Get creative and have fun with this step!
Assemble the coat rack/shelf pieces together with wood glue and brad nails. Attach the hooks to the front.
Take the other half of the cleat and attach it to the wall with screws into studs or wall anchors. Hang and enjoy!