The project should be very quick to cut and assemble with scrap cardboard if you do the folds properly and also if you get the order of operations right. The first time I made this, the flimsy cardboard parts got kind of wily during assembly. The trick is to tape each corner of the tray shelves and apply a bead of glue on the inside (to "pin" it). The other trick is to set the overall form first - by attaching bottom shelf, then top shelf...then infill with middle shelves.
Each unit should be built 20" wide or less. It may be strong enough pile in solid books. But it is even better for random stuff, display, etc. I sold the large shelves on the last page of this instructable to an artist friend who uses it for her stereo, coffee maker, and some found objects. These shelves are so cool because they are built just like carboard boxes - bonus if you can adapt existing tray lids and box corners - then you have no scoring and folding to deal with. Anyway, hope some people actually try this and enjoy~
Step 1: making the tray shelves
So there is no secret about how this is made. Each tray shelf would be either a preassembled shape, like a box lid (or you could cut the top and bottom off of a taped-shut box and get two). You should leave the turned-down tray sides at about 2" for strength. 9-11" is a good depth for the shelves - no wider than you have to.
If you don't have box lids or a few boxes of the same size to make lids out of, but you did rescue a refrigerator box from the trash, you can pretty easily make trays. Cut rectangles 4" wider and longer than you want your shelves to be. Then cut 2" squares out of each corner. Drag a line 2" offset from the edges, to use as a guide for your scoring and folding. I won't go into detail about that here, but you can check out my instructable "cardboard book shelves, like a carpenter" for more info.
After your pieces are cut and scored, fold the tabs over a few times to be sure they are compliant. Tape the corners together with as little tape as possible. You can see from the image that I used way too much. Run a medium bead of hot glue inside each seam where two tabs come together. This is just to hold the shape until they've been glued to the vertical supports/angles.