Draw or download a box joint template appropriate for the scale of your box. If you draw your own, make sure the notches of the box joint are staggered at each mating edge so they will fit together like a zipper. Also make sure the depth of each notch is the exact thickness of the wood you are going to use. That way, when the joints are fitted together perpendicularly, the edge is flush.
Load your design into the computer numeric control (CNC) software interface of the laser cutter. The machine is essentially a plotter, like a printer, with a laser cutting type. To operate, it will require specific types of files. You may have to convert your file type or format to ensure the CNC machine can read it.
Place a sheet of plywood on the CNC bed in the same way you would place a piece of paper in a copier's tray. Make sure the plywood is perfectly flat on the cutting tray. Otherwise, the two-dimensional design will not transfer accurately.
Click the "Start" button on the CNC control interface. Wait while the CNC machine executes the pattern. Remove the pieces when the program is complete and the laser carriage has returned to a resting position.
Apply wood glue to the insides of the notches with a small paint brush, assemble the pieces, then clamp square.