Place a small bead of glue along the joint and then hold the pieces together until the glue sets.
Hot glue comes in varieties with different melting points and strengths.
For hot glue to hold well, you should use the high-temperature, high strength glue sticks. These are yellowish and opaque in appearance. Water-based glues are unsuitable for cardboard. Organic solvent-based contact adhesives can also be used on cardboard.