First, you'll want to take all the doors off of the cabinets and lay them out, cutting enough fabric for each door. You'll also want to unscrew the handles and any other hardware that may still be attached to the doors.
Next, take the fabric and nail it to the cabinet door with sturdy craft push pins. It looks like Veronique used 16 pins total, to secure her fabric.
For the cabinet corners, fold the middle, followed by folding one side flap over and finally folding the other corner in (securing with a pin).
Once the fabric is secure, make the necessary holes on the front side of the door to re-attach the knobs. As for the hinges, Veronique says that when she re-hung her cabinet doors, her hinges were about 1 inch inside the cabinet, so it was easy to just fold or score the fabric to make it fit.
Related How-To Posts
[Images from treschicveronique]