This fabric was found in the sale section at JoAnn's I think it was $2/yd, I grabbed two yards for four drawers. This is also a cotton with a little stretch to it, but I don't think that is necessary.
I took a large piece of cardboard, placed the drawer on top of the cardboard and traced around the drawer. Use an exacto knife to cut out your cardboard, you can keep to the inside of the line traced as you want it to fit inside your drawer.
Cover the cardboard in glue (I used plain crafters glue, but I think this would be a great place to use spray glue). Place the cardboard on top of your fabric. Cut the fabric to size leaving enough to fold over the edges.