Torn. Cut a patch out of cardboard (shirt cardboard will usually do) and apply rubber cement to patch and to area around tear. Let dry. Then apply a second coat of cement to the patch and smooth it down.
Pieces of heavy cardboard separated. Glue together with rubber cement or, better, with Elmer's Glue-All.
Separated from another material. Reglue with rubber cement or Plio-bond cement.