Staging is the most important part of the film making process. That is a bold statement to make, but considering how even mundane, everyday scenes can be made infinitely better with the right staging. It is possible to tell a parallel story with the right staging and all of the titans, as far as film making goes, all the way from Welles, to Kubrick, Eisenstein, to Kurosawa and even modern directors like the Cohen brothers, Lynch, and Tarantino all stand apart in their trade because of the way they set a scene up.
Staging, in the most simplest form is putting actors, props and other things into a scene, their placement and how they fill up the frame. It is a concept picked up from theater and stage plays where the director places each character up in the best way to complement both each other and the story. On stage, it is mostly static and the audience has only one point of view. With cinema, on the other hand, the options are virtually endless.
How to do it
While auteurs of the medium all have their own way to do it, there are no real rules when it comes to staging. Unconventional staging is fine, as long as you are able to tell the best possible version of the story, in every scene. You may like to cut every few seconds and have your shots seem like a set of static, talking pictures, or have every scene carefully planned out, including where each actor should be sat.
Consider this though, real life does not happen nor does it flow with jump cuts between each sentence. Rather, you observe a scene with all the characters in it at once, people act and react in relation to how others in an environment act and react. A scene set up like this is more natural, people act simultaneously and the resulting effect is more organic, engaging, like the audience is actually in the room with those in the story.
Our physical behavior says as much about our emotional state as our words, that is why non verbal ques are so powerful in real life. Appropriate staging does exactly that, it conveys maximum emotion within a scene, far better than a static, talking picture, back and forth between people. Again, the directors mentioned here came up with all that by breaking convention, so stage a scene in a way that you think is best for your story.