I folded the sides in and stapled them down.
scraps of fabric (in my case a scrap from the chair cushions and an old t-shirt)
Mod Podge or Elmer's Glue
scissors to trim
1. Slab a layer of glue on one side.
Drape your fabric over, and rub it smooth.
Trim off the excess fabric.
Repeat on the other side.
3. I trimmed the scrap for the front the width of the box so it would have nice edges.
Then just painted the layer of glue and added the fabric, folding it under and up over the edge.
I am storing my ribbon in the box. So the outside looks nice, and inside it's white trash.
So pretty easy way to make a plain box look nice for storage, and in this case it actually matches the chair.
Some other ideas:screwing on an actual drawer handle through the cardboard
cutting the handle like Ashley at Make It and Love It