This is a pdf that gives the rules for a collaborative storytelling game.
The basic idea is that you need an antagonist who ultimately loses and a protagonist who ultimately wins. People can add details at any time to the game but important details like character names have to be nominated and approved.
The game also includes some base ideas you can work with, including a list of character names. I thought "Johnald Pregnant" was the most amusing antagonist game.
This whole game is thoroughly described, but there's not really a lot to it. I'd imagine that someone focused on storytelling wouldn't need all the rules, and someone really into rules would want more meat. The people I see benefitting from this the most are a mid-sized group of people on a vacation trip where there's not much to do and they want to do storytelling but have a couple of obnoxious people in the group so they lay some rules down on how to proceed.