Does on computer get all the programs dropped onto it and it then fires out data to the rest of the computers and then they process it and then shove it back at the orginal computer

I think so, aren't they usually a process that requires several iterations. So each one is handled by a separate machine. We had a 30 machine render farm at uni. Each machine handled a frame each. So the whole scene would take a 30th of the time to complete (or thereabouts)...