The depth of my bookcase wasn't particularly important, just as long as it was deep enough to hold books and knick-knacks. Therefore I just collected two sets of five boards of identical widths, 5½ inches and 3½ inches, and of sufficient lengths (20 inches). They didn't have to be milled perfectly either, just as long as they fit squarely and weren't too damaged to support weight.
I cut ten 6½ inch braces out of scrap pallet wood to hold the shelves together, adding a bevel to each end to avoid catching anything as it's placed on the underlying shelf. The shelf boards were then placed side by side, clamped and joined on the underside by the braces with wood glue and brads. This is the easiest way to join the shelf boards, but by no means the prettiest or most space efficient. Ideally I would have either found wider planks to make solid shelves, planed the existing wood down and joined them in plies or joined the two planks with biscuits. That being said, I wanted to keep this project as simple as possible to make it more accessible.
Finally, you will want to choose your top and bottom shelves by selecting the two widest shelves (they should all be of similar width, but chances are there will be some wider than the rest). Cut four pieces of wood into 12 x 1½ inch strips, glue and screw them flush with the front and back side of the top and bottom shelves (see picture). Remember to drill a pilot hole for all your screws, you can countersink all the screws by using a bit the same size as your screw head and following the pilot hole in by ⅛ inch prior to screwing in the screw. Placement of the screws are not important except for the ones that will secure the bottom and top shelves to the pipes, those are at 11/16" from where the wood strip meets the shelf bottom (see pictures), place the pilot holes so that they are not blocked by your braces.
Ultimately I went with more than two strips of wood to secure the bottom shelf because I couldn't get good screw placement with just one.