The basic idea is that he used differing amounts of transparent plates stacked on top of each other to create lighter or darker shades of color. A tall stack of plates would make a darker color; a shorter stack would make a lighter color. It appears he went through a fairly lengthy trial and error process to figure out how to make this work out. One interesting problem that he encountered was shadows from tall stacks of plates disrupting the clarity of the image. You can read about this process of trial and error on his blog, here and here. The latter entry also includes a very ingenious solution for shaking loose 1x1 round plates onto a baseplate in such a way that you can press another plate down onto them and have them stick 32 at a time.
I think it was this idea of stacking transparent plates to change shades of colors that lead to later attempts of stacking plates in different colors to try to achieve a greater color palette. I plan to examine some of these attempts in the future.