How do anthropologists (researchers?) recreate entire skeletons of ancient creatures using only a few bones?

The question was spawned from this news article and namely the top image. I'm assuming the brown are known (found) bones, whereas the white are recreated. My first thought was "why do they think there's another piece of spine at the bottom?" then I realized that there are a ton of areas there that aren't exactly clear as to how they would be assumed. It looks like nearly the entire rib cage is hypothesized.

I'm curious if there is a procedure or actual method to recreating the skeleton.

Thank you