Exposition is necessary to set up a story. In mediocre movies like “Batman vs. Superman,” they simply skip most exposition and assume you know the characters from previous movies, which is simply a lazy and inexcusable way to write a screenplay. In good movies, exposition slips into the story by being interesting in itself and by being relevant later in the story to justify its existence in the first place.
In “The Big Short,” they solved the problem of explaining complex financial deals by simply having celebrities explain them in odd situations. Actress Margot Robbie is taking a bubble bath as she explains a complex financial transaction and Selena Gomez is gambling in a casino while she explains a different complex financial transaction. Because you have celebrities in visually interesting situations, it makes the exposition interesting to hear as well.
Of course, most movies can’t rely on putting celebrities in interesting visual situations, so the more common way to present exposition is by being subtle. In “Thelma and Louise,” Thelma is packing to go on a weekend outing with Louise. As she’s packing, Thelma picks up a gun, holds it like holding a rat by the tail, and dumps it in her purse. She could have just grabbed a gun and dumped it in her purse but that’s too common. By holding the gun with such distaste, she highlights the gun without making it too obvious.
“The Karate Kid” gives another example of introducing information by making it interesting when the apartment handyman teaches the hero to do something seemingly simple (waxing a car or taking his jacket on and off in the remake). This simple but odd behavior is memorable because it appears to make no sense. Later when the hero rebels, the handyman reveals that the hero was actually learning a self-defense technique.
In both “The Karate Kid” and “Thelma and Louise,” exposition is introduced in a visually interesting manner that makes us remember it. Then it reveals the importance of this exposition later through conflict.
In “Thelma and Louise,” this occurs when Louise uses the gun to shoot Thelma’s would-be rapist. In “The Karate Kid,” this occurs when the hero rebels against the handyman and is astonished when the handyman shows him how seemingly trivial movements are actually self-defense techniques.
So the key to revealing important exposition is to make it memorable at first while appearing trivial, and then reveal its importance through conflict later.
In “Zootopia,” the hero is a bunny who wants to be a police officer. While chasing a criminal through a rodent village, she saves a female rat from getting crushed. Then this pays off later when the female rat turns out to be the daughter of a rat mobster who then decides to save the hero bunny.
So set up important information by making it memorable, but disguise it so it also appears trivial. Then pay it off later through conflict.