How to attach a drawer without screwing?
Easy:
Make a box that is about the size of the space.  The front should fit fairly close.  The box itself should have about 1/4&quot; spacing all around it.  That's 1/2&quot; narrower than the opening and 1/2 shorter than the opening is tall.
On the back side pieces put felt furniture glides top and bottom. On the front put them on the bottom of the space.
In use the front of the drawer rides on the felts at the front of the space.  The back of the drawer rides on either set of felts depending on the combination of upward force (most of us lift a drawer while pulling it) and the amount of drawer in the space.
When you move, set a hot water bottle on the felt for 20 minutes.  It should peel off easily.  If there is adhesive residue try goo-gone, or mineral spirits.
The glides I'm referring to are 1/8 to 3/16&quot; thick made of beige felt.  One side is adhesive with a protective paper on it.