From a mouse pad killer: Get a bottle of rubber cement. On the underside of the mat, paint out a line along each side, near the edge but not at it (helps keep it from slipping away). If you need extra grip, paint a 1″ (2.5cm) circle at each corner. Allow it to dry upside down (this will allow the rubber cement to flatten out under gravity as it cures) for a few hours. Flip it over, and it won’t go anywhere.

What about hot glue?

Hot glue will rub off… rubber cement will be thin and hold well. I’ve done this my self.