To further mine the cliché; Film is a visual medium. When writing a script you become a visual storyteller, not a novelist or a playwright. Audiences want to see the world of the story and the events that drive character's actions. Unfortunately, we often need some exposition to ensure that those same audiences aren't completely confused, and that is where many people run into trouble. It's very easy to spoon feed information, but it's incredibly boring and insulting to your audience to do so. You need to keep them engaged, but how do you balance information and action?
If at all possible eliminate the need for exposition. Go back and tweak a few things, make it so that we see everything that we need to know occurring in the script. This is one of the benefits of coming in late and getting out early: We see the bare minimum that we need to understand what is happening and we hop forward, landing on key beats. There's no room for lollygagging.
Let's say that there is no way around having some exposition in there. That's fine, most scripts have it. You just have to write it well. Keep your exposition as short as possible. Give only the bare minimum amount of information that is needed for the audience to understand what is happening, and have that information propel your characters forward in their journey. It should go without saying that characters should not be discussing info that is incredibly obvious or known by all.
Don't give exposition right away if there is a way for you to deliver that information later on in the script. It's good for your audience to have questions as long as they can follow the story. It makes them engaged and they experience events along with your characters as they too search for answers. It's always satisfying when the answer to a question is found, and your audience will appreciate it.
Every Briefing Scene Ever
The easiest way I have found to deliver exposition is through an authority figure. It makes sense if a judge is explaining a case in a courtroom or if a federal agent is giving an intelligence briefing. We are spoon feeding information but it feels natural because of how those scenes are framed. It is important to keep people's interest, however. Don't just have your authority figure stare into the camera delivering information. Show how your protagonist and their compatriots are taking in the information, talking amongst themselves, or perhaps there is some debate in the room that causes tension.
Another method is to distract from the fact that information is being given. Have your exposition appear in scenes of great emotional conflict. Perhaps background information is used as ammunition in a heated fight, or a character is emotionally broken down and lets out the truth behind a past event. The audience will be so entranced with the drama unfolding before them that they won't even register that they have been given a bit of crafty exposition. If you're a comedy writer, hide exposition in a particularly funny scene for a similar effect. As long as the audience is engaged and entertained, they won't notice!
A Plea from the Author
This is more of a personal note from me: Please don't have a newscast or newspaper reveal exposition. You never want anything in your script to be incredibly convenient, and turning on a television at just the right time to hear a specific news segment that pertains to the story is one of the most convenient things that I have found in scripts. If there's a newspaper headline in your script and it doesn't say "The Dead Walk," I ain't interested.