Sweep a concrete floor or surface with a broom. Choose a surface that is exposed to direct sunlight -- such as a patio or driveway. Fill a mop bucket with hot water and 1 tablespoon of bleach. Mop the surface to rid the area of dirt, grime and other contaminants. Allow the surface area to completely dry before moving on.
Place the rug facedown on the clean floor surface and leave it there for 36 hours. Direct sunlight will naturally rid the rug of wrinkles. The facedown position prevents the colors of the rug from fading.
Turn on a hair dryer. Hold the barrel of the dryer 12 inches from the back side of the rug. Move the hair dryer slowly back and forth over intensely wrinkled areas until the fabric is smooth and flat.
Take the rug inside. Lay a non-skid, rubber-based rug runner pad on the space in which you intend to place the rug. Position the rug over the pad. Runner pads prevent rugs from inadvertent bunching or buckling.
Center a vacuum cleaner atop the rug. Start the vacuum. Vacuum from the center of the rug outward, remaining 6 to 12 inches from all edges. Vacuum the edges of the rug with a suction hose. Avoid rolling the head of the vacuum over the rug edges to prevent curling and wrinkling.