Make sure your table placemats are free of any oils or dirt. Residue could keep the rhinestones from sticking to them properly.
Pick up a single rhinestone using a pair of tweezers. Since rhinestones are small enough to slip between your fingers, it's best to use a sharp pair of tweezers when working with them. Hold the rhinestone so that you can see the flat backside of it.
Use your free hand to dab a cotton swab in craft glue. Cover the backside of the rhinestone in the craft glue, using just enough to coat it.
Place the rhinestone onto the placemat with the glue side facing down. Position the stones so that they won't interfere with a dish or utensil that might sit atop the placemat. To be safe, create a rhinestone border around the edges of the mat, or create a design in the corners. Wait at least 24 hours before using the placemat to ensure that the craft glue has fully dried.