Here is a tutorial with a few different techniques and approaches for green screen cinematography.
Just Some Green Cinematography
Green screen cinematography is different than most other types of digital video cinematography because it is designed to capture the subjects in position according to a specific shade that is then used in post-production. The process of using the green screen is called Chroma Key, and involves replacing and compositing another image where the green was recorded. To do this effectively you have to capture the green screen with your cinematography so that it can actually go through this compositing process later on, and if it is not recorded properly the green screen will not be able to be addressed and removed correctly. Here is a tutorial with some green screen cinematography tips to make sure that you get it right the first time.
Green Screen Lighting
Lighting is one of the most important elements of all cinematography, and what many cinematography tutorials focus on, it is also important in green screen cinematography. The first thing that you are going to have to remember with the lighting is that it has to be completely even. The Chroma Key process is going to identify one single color and allow you to composite with it, but if there are different shades of green in different parts it is going to cause problems in this image. You are going to want to use soft lights here, and oftentimes many of them, until you get it even. This is going to require that you use a spot meter for lighting on different spots around the green screen, as well as the regular color readings.
You are also going to want to make sure that the lighting is bright enough to really bring out the right green that is easiest to use during compositing. This is a color that is not commonly worn by people and is not going to be easily matched in the rest of the scene objects, so it stands out on its own. This means that you have to light the green screen sufficiently so that the kind of color is produced that is not going to end up anywhere else, which would then be composited out.
When framing the image for green screen cinematography you are going to have to position the subjects in front of the green screen differently than you would in a normal scene. First, you have to position them further away from the green screen than you would with other backgrounds. This is done so that the light from the green screen does not bounce onto the subject, that would bring the green color onto them.
You are going to also have to make sure that the green screen remains a flat image covering the entire back of the scene in every shot, at every angle. This is a difficult proposition since the green screen is only going to take up one clean wall, and when you are getting other angles and close-ups they will not actually have the green screen in the shots as they may have had with the straight ahead master shot. What you actually have to do with green screen cinematography to address this situation is to "cheat" the shots, which means that each individual shot and the objects in the shot will be positioned on their own away from the original geography. This will be done to satisfy the perceived geography of the story space, but not the actual geography.