Measure the rug and purchase a same-sized non-slip carpet pad online or from a home improvement store. Place it beneath the rug to secure it in place.
Cut squares or strips from a roll of double-sided tape, and attach them around the perimeter of the underside of the rug. Remove the paper backing from each strip, set the rug in place, and push around the edges of the rug to secure it to the carpet.
Rearrange the room to place furniture on or along the edges of the carpet. For example, you could tuck one side of the rug beneath the feet of your couch and set a coffee table in the center of it.