I manufactured and constructed this item at TechShop.
Step 1: The first thing you should do is consider the final look you want
In my case I wanted a long thin modern LED fixture, about 1" thick and 8" long or so. It is used to widely illuminate the space behind my monitors, but it needed to look nice. Many other uses could be had for this sort of box, including direct illumination of crafts, bookshelves, or other personal items. It's super-low-power so it's very safe.
Once the general shape is known, you determine the materials that build up to create your item, when using this process. This box has a mixed profile (where different widths exist and sections which might be hard to carve or cut out of one piece of material), so a good way to do this it to 'slice' your design and cut out the different slices, then glue them together. In my case I had a bottom section and walls which were different, and I also chose this method because thinner material is a lot less expensive than thicker material to do the same thing. Finally, carving deep sections in wood is not as easy with the laser cutter -- it's much better at cutting straight through, so again I chose the slice method.
Also, choose the material for the box layers - I chose a nice 1/4" birch plywood which was inexpensive and at a thickness very easy to cut. More on this later. You could choose anything the laser can cut including wood, wood products like MDF, acrylics of all colors and even glass; but, the construction technique I used was glue, so wood makes the most sense. I won't cover constructing plastic or glass items here, but there's more data on this online.