Buy puzzle glue at a craft store or online (see Resources section). It is best to buy liquid-based glue, as powder-based glue can be difficult to mix. If an applicator isn't included with the glue, buy a sponge brush.
Find a hard surface, ideally a flat table or a kitchen countertop. Put down a sheet of wax paper that is larger than the puzzle. This will help protect the tabletop.
Apply the glue with the applicator to the front of the puzzle in a thin, even coat. Check the packaging to see how long it will take for the glue to dry.
After the first layer of glue has dried, add another layer for extra strength. If you notice that the puzzle has begun to curl, apply a layer of glue to the back. This will help make the puzzle flat again.