To make fabric ATCs, I generally layer a couple of pieces of interfacing together- using a glue stick to hold them together. One of these days, my stash of interfacing (from back in the clothing making days) will run out and I'll buy some of that cool Timtex or Peltex that everyone else uses. Until then, I just stack up two or three layers of interfacing and then put a piece of fabric on top. Usually, I am machine stitching the card design, so that comes next. Then I do any hand sewing and beading. Next I stamp up a bunch of ATC sized pieces of fabric, using a stamp I bought from European Papers. I stick the back on the card using glue stick, and zig zag around the edges. (Putting the back on after the sewing hides the knots and messiness.) The little bits of frayed fabric that tend to stick out bother me, so I zig zag around several times- slightly increasing the width of the zig zag each time around.
Here is a picture of the backs of examples from the last several sets of cards that I have made. The upper left card is from the only paper card set I have done. Boy, that was much simpler! No layering, no stitching...just glueing and stamping.