How to get clean plate from moving footage?
There are a couple of techniques:


A motion controlled camera - The camera is on some sort of rig connected to a computer. The computer is programmed to move the camera in a particular way. The camera runs through the moves without the actors, generating a clean set of plates. Then it is run again with the actors, usually wearing green or blue costumes or parts of costumes. For example, in "Forest Gump," one character loses his legs in a war. The actor had working legs, as shown early in the movie, and in some later scenes wore blue stockings that were composited out. (They also used other techniques, such as simply hiding his legs under various things in some scenes. Whatever works!)
As you surmise, sometimes a larger scene is filmed with a locked-off camera to get a clean plate, then during editing, they zoom into the scene and pan around in software to create the motion you see on screen. This doesn't work well for anything that involves the camera rotating, but can work for scenes where the camera trucks.
Parts of the scenery that the actors are in front of are blocked off with green screens and recreated in post. I've seen outtakes of a few pieces where they did this. If you have the DVD of "The Others" with Nicole Kidman, the "DVD Extras" show how fog was added to scenes that were filmed without it. It basically involved someone walking around behind her holding a large green board. Then, they recreated the scenery in the computer, added fog to it, and replaced the green screen with the foggy scene. I have a vague recollection of them doing something similar in the HBO mini-series John Adams. This would likely involve cameras that record their motion. The motion is then imported into the computer and used to move the virtual camera around the scene they've recreated.