hi , I am scott and i am new to this site .
my question is how do you tell if a game works with a keyboard + mouse , or controller , or both?

PC games here usually works on M+K, with some small exception like Brothers: A Tale of Two Sons. But GOG does describe on the game features if a game must need a controller

Game that supports controller have "Controller Support" on the game feature area of their storefront. Here's a quick look of all game that supports controller here: https://www.gog.com/games?feature=controller_support&sort=popularity&page=1

I agree that it can be tricky.
Like Zlaywal said though, it is marked. That doesn't tell you how well it is implemented though.
I use Mouse and Keyboard exclusively myself, and most modern games, or fashion indies, have their game made for controllers first and M&KB secondly.
I tend to read the forums and reviews, and even go outside of GOG to get a better overview.
You do have to put in some work to become better informed.
If only Reviews mentioned gameplay more, instead of putting the focus on story and graphics.