You hit the dice with the ball, this gives you points totalling the number of pips shown on the dice you've hit, after each hit the die is rerolled. After your ball has fallen you get to upgrade any given "regular" die face to a new custom face. The custom die faces all have a value that you always get when you hit them directly(green) and some that occur when synergizing with already present items(which are spawned by the custom faces) as the die is hit(orange). When you reach the point total in the corner the round ends and you get a new default die(along with six new balls).
You win by picking faces that synergize well together and by picking paths that hit many dice. The game suggests a "best path" in the middle of the green arch which lights up, however because you get a point bonus for shooting outside the arch you should still look around and see for yourself which is best.
I suggest not picking so many explosion faces as they destroy things which otherwise give points.