Dialogue. A conversation between two or more characters allows for simple and effective exposition in a single scene.
Narration. Narration, or voiceover, is a way to communicate a character’s true thoughts and desires, or give omniscient insight into a situation.
Mise-en-scène. Mise-en-scène are props and other things that are seen, but not heard, in a scene. These details, while seemingly subtle, can convey a significant amount of information in a short amount of time.
Text or title cards. Perhaps the most straightforward method, text or title cards can contain all the relevant information your audience will need to know, before the film even begins.
Flashback. There are multiple ways to convey past events in a present narrative, but flashbacks are the most visual as they place your character in context (versus having them simply recount the event, as they might in dialogue or narration).