Step 1:
I used 3/4" thick plywood. I'll protect it from the elements with paint. The box needs two sides that measure 11 3/4" deep. Their top edges need to taper: they measured 29" on the longest side and 18" on the shortest side.
Step 2:
The box goes together quickly with 3" screws. Even Abigail (age 7) got into the act. The bottom of the box (and the shelf) were 27 1/2" x 11 3/4".
Step 3:
The main assembly is ready for a back. I used 1/4" thick plywood, which is plenty strong.
Step 4:
The easiest way to attach the back is to tip the box onto its front. Then you can drive screws directly into the 1/4" ply and into the 3/4" plywood parts of the box.
Step 5:
The roof is made from a single piece of 3/4" plywood I gave it a little bit of an overhang on the front and back edges. Its overall measurements with 32"x18".
Step 6:
The box could might mounted in any number of ways- I decided to attach a quartet of 2"x2" "stilts" to the corners. This is because they were laying around with no other pressing purpose. I liked the height that the box was at when it was perched on my bench, so I was able to attach the legs by simply letting the box overhang the bench top and then screwing the legs to the box. A clamp helped hold the legs in place temporarily.
Step 7:
These doors feature "euro-style" hinges that are commonly found in kitchen cabinets. That said, if your doors don't already have hinges like these, you may want to go with a simpler style- there is a bit of a learning curve to this type of hinge. If you're looking for some old cabinet doors, I suggest checking someplace in your area that offers salvaged and reused building materials.
The doors- once I cut the plexiglas and get it in- go a long way toward protecting the books and the interior surfaces of the box; the other key weather proofer is some kind of decent roofing material.
Also: the term "Little Free Library" is an official designation. There are over 36,000 LFL's in the US alone. You can register your book box and receive a plaque which certifies it as a part of the network. That said, you are under no obligation to do so.