Remove the area rug from the carpet and lay it out on a clean concrete or wooden surface. Use carpet tape, found at any home improvement store, to secure the area on the surface. Make sure to pull each edge as you tape it to ensure the rug is tight.
Set a steam iron to the "wool" setting and allow it to heat. Carefully steam iron the entire area rug, using a towel in between the iron and the rug to avoid burns. Pay special attention to the areas where the wrinkles run deep, slowly gliding the steam iron around the area until the wrinkle lets up. Go over all the edges and corners to discourage the rug from curling. Allow rug to sit for at least fifteen minutes.
Remove the carpet tape and carry the area rug back to the carpet where it belongs. Make sure all ends lay flat on the floor.