Is there a certain amount of space needed in order to use the Kinect? How much of an area do you need to move around in?
Yes, there is a minimum amount of space required:
A bit more practical advice is offered by this article:
In "real life terms," my couch is far enough away from my TV that I can pull a queen sized sofa bed out of it without having to move it and still walk between the bed and the TV stand. I still have to move the couch 2-3' back from where it sits to play with the Kinect, and that just barely makes it happy. If you've got a coffee table or anything else between your couch and your TV, you're going to have to move it as well.