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.
Step 2: Cutting Vertical Supports and Assembling
Your vertical supports are just 6" wide single-ply corrugated. Mine were 42" long but you may find something different. Tip: bike shops and appliance stores. Most of them are happy to give away their cardboard, and some resell it. So just cut 6" strips, score along the middle, and fold a few times. Remember scoring a material with 1/8" thickness means cutting a v-groove or trough roughly 1/8" wide.
Mark the vertical supports before gluing anything to them. Start with the bottom shelf, one corner at a time. The integrity of the whole unit depends on the first shelf being square to the supports, so use a carpenter's square or a piece of cardboard cut square as a guide. Experimenting on a scrap, try two types of hot glue joint - one is a 3/4" puddle, the other - draw a circle with the glue bead, about 1 1/2" in diameter. The puddle is concentrated in one place, so heat and glue penetrates into the cardboard. It gives you more time to adjust to square, but you will still be waiting once you have it in place. The circle covers a wider area, and if you can align quickly, this will be very strong. The reason for blue tape in the image is that I tried to use wood glue for this one - mistake.
Now that you have the bottom shelf in, but it still seems very flimsy, this can barely stand on its own, how could it possibly support your stuff? Keep going, you'll see. Install the top shelf in the same way as the bottom. When you install the top shelf, thats your last chance to fix any crookedness from the bottom shelf. The middle shelves go in a little differently. Fit one of them snugly in its final place. Nose the tip of the gun into each seam and squirt some glue in, and press each seam tight. This is enough. Once you have all shelves in, the whole system becomes a collection of small boxes, and it's pretty rigid. These units can be ganged together to make larger shelves.