The case components are each molded as a single piece, not glued from flat sheets. They're dirt cheap to purchase already made; you'll go through a lot of work to make one from scratch. Consider just buying one (or a package of them when they're practically given away on sale).
If your goal is making one from scratch, solvent welding would be the way to do it without marring the plastic with excess glue. The edges to be joined need to be very smooth and mate together well. Typically, the edge of one piece is butted against the face or edge of another piece. A micro-pipette is used to allow capillary action to draw a tiny amount of solvent into the joint (which requires good mating for capillary action to work), which chemically welds the surfaces together. Lucite objects are often assembled this way.
I've had good luck with this product available from Micro-Mark, I assume you can get the same or similar at hobby stores or from a retailer like Amazon:
The solvent needs to be appropriate for the type of plastic you're using. The applicator is a glass capillary tube with an extremely fine metal capillary tube attached. You dip the applicator in the solvent and the solvent is drawn into the tube. Then you touch the tip to the joint and solvent is drawn between the mating surfaces (and nowhere else).