How does one export a 3D Studio animated model to OBJ format (if possible)? What will be the resulting file like? How would I read that?
No, .obj files do not support animation.
You can check the .obj specification for details of what it does support.
You could potentially export one .obj per frame, but that would be cumbersome. Depending on the tools, it may be possible to export one .obj per keyframe.