Turn the rug over, and roll it up. Reverse roll it in this manner until it is halfway rolled up, and then leave it in that position for 15 minutes. Unroll the rug, and then reverse roll the other half of the rug. Again, leave it rolled up for 15 minutes. Unroll it and lay it flat. If the edges are only slightly curling, you can reverse roll the edges rather than half the length of the rug.
Set an iron on the "wool" setting and iron the curling edges flat. This works best on curling corners on a small area rug. If the rug has latex backing, make sure the iron is not too hot or the rubber will melt.
Secure the rug and fix the curling edges by adhering it to the floor with double-sided tape or adhesive Velcro. This works best on area rugs on tile or hardwood floors. Keep in mind that the tape or Velcro may be difficult to remove later if you want to move the rug to a new location.