Its been a while of checking the rules, but really most of the actual rolling is got out of the way at the start, and it just decides who the player's characters are to each other and general scene setting details, like macguffins and locations.
Act 1; Each player gets two scenes where they generally decide what they entail, then the other players decide the outcome, each one passing you a die, a white one represents positive outcome, black ones represents negative outcome. Things get acted out in freeform (it's a narrative based game of improv on the tabletop).
Then, in the following Tilt phase, through us rolling, we decide who will add two new categories to advance the story. This is pretty much decided by who rolls highest using their white dice and who has the highest total with their black dice.
Act 2 is the same as Act 1, but players assign the outcome dice to themselves, I believe.
The Aftermath is similar to the Tilt, though people roll on a pregenerated Aftermath table.
Then players take it in turns to narrate the closing montage (in freeform), which are longer with the more players involved.
It's actually way simpler than it made it sound and the dice rolling is fairly unobtrusive and serves as a way to decide how scenes work towards the endgame.