You will need knowledge of CAD/CAM and access to a laser cutter (obviously).
The design file is on 123dapp.com, here's the link:
Things you need:
Glue (tensol, araldyte)
Door Knob (optional)
Step 1: Designing the drawer, the front
You must choose what size you would like the drawer to be. For example if you want it to be a cube measuring 80x80x80mm then you should start by making a box size 80x80mm on your CAD program.
Then you must check what thickness your acrylic sheet is, mine was 3mm. This is the tricky part, you need to make the puzzle joints at the edges of the square. To do this draw a line 3mm (or the thickness of your acrylic) from the edge on the inside and then make perpendicular lines across both vertical lines every 10mm.
You should end up with something like the second picture. Next you must delete some sections of the lines to make the puzzle shape. Using the delete section tool, delete the overhanging lines then delete parts of the vertical lines to make a zigzag shape like in the fourth picture.
You need to do this around three of the edges, leaving one for the top of the drawer.
You may add a hole in the middle to screw a door knob to the drawer to make it easier or a large hole so you can open it with your finger.