Look over the dresser and identify any joints that will require repair. Separate the joints as much as you can and sand the adjoining surfaces lightly with a fine-grit sanding block to remove the old glue from the surface of the wood.
Wipe off the sanded areas of the dresser parts with a tack cloth to remove the dust left from sanding. Apply a bead of glue to both surfaces of the joint where they contact each other and press the parts together.
Clamp the dresser parts together with a wood clamp. Wash off any excess glue that oozes out from the joints with a damp rag. Allow the glue to dry 24 hours and remove the clamp.