How do you reupholster a "click-clack" futon?

I have a very small, black click clack futon couch. Its almost exactly like this futon at target http://www.target.com/p/Sofa-Bed-Black/-/A-12184769 I've tackled very small reupholstering jobs before, but nothing as big as this. My main worry is that it has moving parts(back rest folds all the way down, as do the arm rests to create a platform bed), and the fabric having enough slack to do this on a regular basis. At the same time I don't want the new fabric to look saggy when the futon is in the couch position. Also I would like to add more cushioning to make it more comfortable, but don't know how to. Has any one done this before with this kind of futon?  I appreciate any advice, or suggestions.

Take apart what you already have very carefully, and measure the pieces ?