For me it's mostly experience I think.
When you play enough games you start seeing patterns emerge between trashers, gainers, drawers, etc.
But oddly enough, this pattern recognition (and not looking at the entire board) can also be a reason that you might hit your ceiling.
I also started seeing my deck in a sort of Matrix style flow, I knew without thinking about it which cards I had seen, which were in my deck etc and for my opponent too, I'd think: "his X must be coming around now", and often I'd be right. This helps tremendously with cards like Possession.
I didn't have to add individual Treasures anymore, I instantly knew the amount I had to spend, even with Bank.
I don't want to say that I was becoming the almighty Dominion God who could see the game on a whole other level, but as you progress as a player and start getting more and more experienced, tedious tasks like tracking cards and adding numbers becomes second nature, so you can divert more attention to the current game state and how to work from there.
I'm sure experienced players will recognize this.