I assume the lucite pieces are glued together, as there are no visible screws holding the pieces together. Some sort of epoxy probably.
They have one size that obviously works well for deer, but they can make any size you want. The good news is that these guys are hunters, so they speak our language.
The installation is simple, rugged enough and easy. There is a hole drilled in the top piece of lucite, and a 1/4" bolt is used to hold the skull in place. It's one of those drywall type bolts that has the wings on the nut that spread out inside the skull.
You simply fold in the two wings on the bolt, and slide it inside the skull. Then you tighten the bolt up against the back-side of the top lucite piece, the wings spread out inside the brain cavity, and they hold the skull nicely. You don't want to let your kids play with them, but for the intended purpose, they hold the skulls in place nicely.
FYI - they look a lot more "expensive" in person than the $30 price would leave you to believe.