Can anybody explain how the match "grades" work?

There are three large factors: Your (hidden) rank How well you did with that champion relative to everyone else who plays that champion How well you did in that game relative to everyone else in that game

It seems to be a combination of objective control and KDA, as you can only achieve one to get, say, A rank, but you tend to need both to consistently obtain S ranked. This allows supports to get S ranked if they are present for objectives and get their assists, along with generally taking care of vision properly.