The first step is to first orient the penny cut out to match your souvenir.  I actually have pennies with both orientation, so you will likely need to do this step.  Just rotate the oval cutout and reposition it to fit within the design as shown. 

Before assembly, I will test fit the penny.  I made the cutout a little bit bigger than the normal penny size, but you never know , so it is a good idea to test fit it all.

Next, add a thin layer of wood glue to the back of the map piece.  It won't take much.  I also will take either my finger or a small brush to smear the glue to ensure it covers all of the surface area.  If you have any glue squeeze out, just use a damp cloth or a sponge to wipe it away as soon as up assemble the parts.  The sooner the better. 

• I use Gorilla wood glue, but any general purpose wood glue would be fine. 

The last step is to add in the penny.  You could use some hot glue to attach it, or you could just drop it in the slot.  It depends on how tight the fit is and if you want to remove it regularly.  Most souvenir pennies do not have anything stamped on the back, so attaching it would be fine.