After recording the ripples of passing gravity waves I would imagine that some high-power math would be required to derive information about the sizes, spin, and distance of the merging black holes. Is it possible to get some insight into how they figured out one was 31 solar masses and the other was 20? How do you "see" spin from a wave?
One element of the answer is that they do it in the other direction. They simulate many different possible black hole mergers and then look for the nearest matches to what they observe. I imagine there is some scope for interpolating between the simulations as well as running bespoke simulations to confirm the match. Spin affects the wave because the shape of space around a spinning black hole is different from that around a non-spinning one, which affects both the motion of the black holes and the processes by which the gravitational waves are radiated.