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Multiple cameras are usually setup around the area of interest and synchronized to shoot at the same time. This was done in The Matrix using some Chroma keying (what's typically referred to as Green Screening or blue screening) although an earlier use of it was done with a horse wayback when with black and white photography in an attempt to proove that there is a moment when all four of the horse's hooves are off the ground at one point in time.
Around the time of The Matrix's release this was also used in a car commercial along with some chroma keying again where a kid tossed a cheese puff/ball into the air whil this guy commented on the interior. So in answer to your question they used the time track photography/videography to record things from multiple angles. But they also used some Chroma Keying (green screen) so they could composite someone moving in realtime.
The green is usually omitted in favor of whatever is in the other videostream essentially since they aren't necessairly there they have to mime or pretend they are. But even then time track photography/videography has to be used so that they are convincgly portrayed as being there. So then the question becomes how come you don't see the cameras? The answer they most likely paint or block them out with the same color so that they too are omitted in favor of the stream that actually has a background.
Also for this to really work you need a green room not just a green screen. One screen alone won't work so well with time track photography/videography is this is what you intend to do. A whole room of green/blue is
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