Step 1: Download and Laserize
If you just want to get yourself a pair of perspective flipping goggles, all you have to do is download the file, arrange the parts to be cut (being sure to include two earpieces, they're identical, you know) and laser cut yourself a pair (mirror side down on the plastic, please.) It's pretty simple.
What those of you without laser cutters (poor souls that you are) may take away is this cool construction method I learned from puzzle maker Lee Krasnow. I measured my screws, nuts, and washers, and modeled them simply in cad. I measured the width of my plexiglass. Knowing those dimensions, I could make some tabs in the design. When the design is put together, the tabs keep the different panels aligned and square to one another. the screws fit down through the holes, and connect with the nuts in the adjacent panel. The nuts are held fixed by their tight fitting in the plastic. Putting these together is a breeze, really.
Step 2: See?
These are just a fancy version of holding a mirror underneath your eyes and looking down into it. The effect is pretty cool, but the design could use a little more tweaking to be perfect.
I went through a lot of revisions in the design, testing and prototyping the model before reaching a final product. The laser cutter made it easy to test new revisions on the spot.
Step 3: Cool.