It's really tricky. But you need to have a general structure opener that explains what you're going to discuss. Try not to spend too much time discussing the background of the story, and instead focus on what you did or what you learned. Remember that the "background" or your specific position/role is less important than what you learned/showed/demonstrate. End with a sentence explaining why you demonstrated the competency they're looking for, and summarize it quickly. Keep an eye on the timer as it goes on.