Use a 1/8" square or fishtail endmill to mill the walls for the box set. A 3/4" or taller material will be best for making a functional box. Use double sided tape to keep the nesting sections from shifting
Use this EASEL "link":http://easel.inventables.com/projects/lAJaBMX0xuvjf2M53-PReA
Choose a 1/8" material to use as your lid. Expanded PVC cuts quickly and comes in good colors. A translucent acrylic also works really well.
Use this EASEL "link":http://easel.inventables.com/projects/-3sWlerWnAfqJaCXaHZZyA
Mill the box floors from either the same material as the top, or choose one that compliments it well.
Use this EASEL "link":http://easel.inventables.com/projects/EEZ58NPFcOvP_Rs9rixjzw
If everything cuts correctly, no glue is required for assembly. The base fits into the side with the small ledge cut into it. For extra durability you can squeeze a small amount of super glue into this area.