Although various configurations can be setup via Material Room menus, and can be managed through the Simple interface, this topic is considered Intermediate level.
Intermediate
1) Either I put an object at the relevant place in the scene, and give it a uniform (green) texture,
- The object material should be Ambient only. It should not support Diffuse, Specular, Transparency, Reflection, Bump/Displacement, etc. (unless I want to have the effects of the scene lighting on my backdrop replacement as well)
makes 
The object should not cast shadows (unless I want them on my backdrop replacement as well), nor should it act as a light emitter in IDL lighting conditions, nor should it be visible in raytracing (reflections!). Those properties should be switched OFF.
2) Or without any object obstructing the background, I export my image in a format which supports transparency (like PNG),
3) Or without any object obstructing the background, I activate Background Color and assign it an appropriate color.
Either 
Or 
Or 
will do the job.
See the overview on the background nodes in general.