Cut out all the pieces of 1-by-4 to the dimensions listed. You should be able to get it all out of one 9 foot long, 16 inch wide 1-by-4.
Stand the two edge pieces so the long sides are vertical. Mark the inside edges of the two side pieces 1/4 inch from the inside front edges.
Glue the front piece in place so that the front sides are aligned with the 1/4 inch recess mark leaving a 1/4 inch reveal on either side of the front. Setting back the front gives the lid a little overhang so you can open it without needing a handle.
Drill pilot holes through the sides and into the edges of the sides of the front piece. Drill inset holes in the pilot holes to allow you to recess the screws.
Glue the ends of the front piece sides to the sides as marked and screw 1 1/4 inch screws into the pilot holes to hold the sides to the front. Tap decorative wood plugs into the holes to disguise the screws.
Turn the assembly on its face and glue the edges of the bottom piece. Set it in place, clamp and allow to set. Then, drill pilot holes through the sides and front and into the edges. Drive the screws. Wipe off any overflow glue with a damp cloth and tap wood plugs into the screw holes.
Place the Masonite pegboard back in place on the rear edges of the bin assembly. Clamp in place and drill pilot holes through the pegboard into the ends of the sides and bottom. Screw the back in place with 3/4 inch screws spaced around the edges.
Mount the 2-inch wide by 13 1/2 inch board across the top of the box along the back edge. Pilot drill the screw holes, glue it in place with two 1-1/4 inch screws in each end to hold it in place. The back strip will give you a place to attach the hinges for the lid.
Lay the lid on top of the box and line it up with the back strip. Lay the hinges in place where you want them and mark around the edges. Use your hammer and chisel to chip out the wood where the hinges will rest. Shave away the wood until the hinge flaps rest flat with the surface of the lid and back strip. Screw into place with the screws that come with the hinges. Seal around the edges of the hinges with wood filler.
Sand the edges of the box and lid, filling any holes and cracks with wood filler. Stain and varnish the box inside and out.