Cinematography question?

It somewhat depends on who the director and cinematographers are- They can be a great couple or a horrible one. But I am assuming you really mean what are their roles rather than how they get along.

The director instructs the cinematographer how the scenes need to be shot and what emotion needs to be gained through the lens, etc. Just like he/she is with the actors, the director can be extremely direct and give clear instructions on what needs to be done, or the sort that wants the artist to help put in input. Sometimes the director will leave lighting choices to the cameramen- sometimes they will get very specific to fit the script and/or their interpretation of the script. There are also well know, and well trusted cinematographers, for instance Caleb Deschanel (father of Zooey Deschanel), who is very known for films like The Right Stuff, The Natural, Fly Away Home, The Patriot, and The Passion of the Christ- Films like this make Deschanel a sound enough artist that a director like William Friedkin brings him in to do a film like The Hunted- probably not giving him the breathe down the neck instruction, but fully trusting his sense of the scene.

Directors like Steven Soderbergh however are known to love to take the camera into their own hands and I would have a hard time envisioning these two great artists like these getting along well together on a set. I would imagine them fighting over the camera- or more likely- the Cinematographer getting pissed off after the camera is take from him/her- especially if the footage is not of their liking. At the end of the film making, often directors take over cameras, and, unlike Soderbergh, who shoots well, shoot horribly to get "what they want." But when the film is view this mistake is credited to the cinematographer not the director.

Usually most of it is worked out in previsualizations and storyboarding so the director is free to work with the actors on performance.

Check out the "Ask a Cinematographer - by Oliver Stapleton" on imdb:

http://us.imdb.com/indie/ask-archive-toc