One of the most popular ways to create a 3 dimensional assembly of waterjet cut parts is via the t-nut technique. In this technique, a bolt or screw is passed through a round hole on the faces of one waterjet cut part, and then through a special slot perpendicular to the cut edge of another piece. The bolt is threaded through a nut which is held in place in a perpendicular slot.
The mating edges of both parts are usually cut with tabs and slots to further secure them together. This is similar to the finger joint or comb joint sometimes found in woodworking.
The slots cut into the face can be placed along the edge for maximum space savings. For more stability, the slots should be surrounded by solid material. This is analogous to the mortice and tenon joint of woodworking.
Note that the slot which holds the bolt is extends slightly beyond the nut. This is to make sure that the bolt fully engages all the threads on the nut. It also gives some flexibility in the length of the bolt used.
You might need to consider making the tabs slightly smaller than the slots or overcutting the corners in order to compensate for rounded inside corners due to the waterjet’s kerf. (See my earlier post on this subject).
Since the cut edge of the is used in contact with a flat face, you should consider the use of low-taper waterjet cutting for this type of construction.
Here is a complete box made using this technique. The box sides have been laser cut from clear acrylic, which lets you see how the whole thing is assembled.