There are as many ways to tell stories as there are story tellers. Style and personality are unique to each performer. Yet, there are constants that transcend the individual. Yet, there are standards that should be followed that can make everyone more effective in telling stories. In fact, most great radio shows follow these 5 rules for better stories on the air.
It may not be as in-depth as the Pixar way. The movie company developed a great template of 22 storytelling rules for their writers. But personalities that develop the skills to master just a fraction of those rules can greatly raise their game.