There are various ways to "make boxes" yourself, and various materials you could use.
If you want to use something paper-based... you could use "book board," matte board, cardboard, or sheets of any stiff paper-based materials (cut them into proper sizes and glue them together).
Or use cardstock and fold it into a box shape (origami), possibly covering with some kind of papier mache if you really want to do that too (the surface won't be smooth though without a fair amount of work),....or you could cover another "armature" like fine wire mesh (WireForm, etc.) or even chicken wire, etc.
You might want to check out some of the cool boxes you can make origami-style... great for gifts, etc.... and this page also has other lessons on making boxes from various things:
http://glassattic.com/polymer/boxesgift.htm
For the sturdier boxes, you can also cover purchased pasteboard-type boxes with papier mache, or with other things like polymer clay**, decoupage, paint, etc.
Or you could do the same coverings over those cheap unfinished-wood boxes from Michaels, etc.
**polymer clay can be used to create freestanding boxes from "slabs" of clay, or by forming and baking the clay over another box then removing it... or by covering a permanent box or box armature (a pasteboard box, wire mesh, or actually lots of of other things):
http://glassattic.com/polymer/vessels.htm
HTH,
Diane B.