For the algebraic tilings, with just a few weird shapes with weird angles that somehow work together, they are more discovered than made. They always start with an algebraic root that has strange properties. For example, in 3D space, there is a set of 19 points at power distances, based on the plastic constant. There is a classic adage in math and physics: "If it doesn't work, try 1, 0 or the square root." For algebraic geometry, once you've identified an algebraic root, the square root always seems to simplify things geometrically. That's why I wrote the SqrtSpace function. After discovering that made all of my tilings easy, I went through the literature and looked at all other known substitution tilings to see if there were exceptions. So far, there aren't any exceptions.
For non-algebraic with "many" pieces, things are simpler. For example, with multiples of the 5 tetrominoes (Tetris pieces), make larger copies of each of the tetrominoes. This is then a substitution tiling. But there are many ways to do this.
I still haven't found a 3D substitution tiling with the plastic constant, but I'm fairly sure one exists.