I feel the tiniest bit like Houdini - I came up with a way to make the fabric box with no hand stitching and no seam binding...
Here we go
This is improved version 2.0 of the fabric box I tried to make in my other recent instructable: http://www.instructables.com/id/fabric-covered-storage-box-with-custom-dimensions/. Forget that one and use this one instead. I think its much easier.
Step 1: Materials
seam ripper (aka the "undo button")
remnants of a suitable size to cover the inside and outside surfaces of the box.
enough cardboard or soft sheet plastic for 4 walls and the bottom
scissor sharpener (recommended)