The song format forces you to tell your story without any wasted words, without any superfluous lines. You can't just pile on one one verse after another. No matter how clever a story you're telling, you still have to get to the chorus before people get impatient.
Look for ways to shorten the exposition, to move the story quickly forward while keeping the essential elements.
If you drop verse one, can the listener still tell what's going on? Sometimes cutting things off the beginning of the song is all you need to do.
Familiar cliches can come in handy. They tell the audience what you're getting at without requiring you to fill in all the details.
Lyrics can't afford to be as detailed and nuanced as novels and films, but with the aid of musical gestures they can tell stories that are every bit as powerful. Look at classic story songs to find examples of brilliant and concise storytelling.