Believe it or not, you can get away with nothing more than glue -- ***Amazingly*** strong and super light.
If you use a rubber cement type glue (that won't eat the foam core -- can be hard to find) you apply glue to the edges of the hinge, wipe it off with your fingers and then use the excess on your fingers to know *when* to attach the surfaces. once it goes from liquid to tacky, it's ready. push 'em together and gently hold for a minute or two, then ignore it for an hour. These are great becase they're permanent and insensitive to summer heat.
For hot glue, align the hinge and apply the glue. Then as Bixler says, squeegee it crazy thin. The glue alone could hold it on, if you do both sides, but tape on one and glue on the other works splendidly.