I need specifically to know how to put it together without the sides showing/fraying. When I zig zag the sides of the panels together it just doesn't look right!?

I have sucessfully made 2 of the tissue box covers from skeldale house yahoo group and both were easy to put together. If you join her yahoo group you can download the instructions for this project.
Helen

I have instructions from a Skeldale House design but I can't find the link to the page it's from so I'll explain it.
The sides have satin stitch edges with cotton batting in between. Then the sides are stitched together with a zig zag stitch, then sealed with Fray check or Aileen's Fabric glue.
The top is hand sewn to the sides.