A rug can develop wrinkles if the installers don't give it time to acclimate before installation or if they don't stretch it properly when they install it. Heavy traffic can also make it loosen and bunch up. Once the wrinkling starts, address it promptly, or it will quickly worsen, because shoes catch more easily on loose carpeting. The procedure involves re-stretching the carpet, and to do that, you'll need to rent a carpet stretcher and a knee-kicker. Both tools are available at a rental outlet or building supply center.
Move all the furniture off the carpet and into an adjoining room. For stretching to be effective, the carpet should be completely uncovered.
Remove any metal transition strips or carpet borders to which the carpet is attached. You can usually do this by prying upward with a pry bar and pulling nails with a hammer or pliers as soon as they pop out. Be careful not to bend the metal. You don't have to remove any baseboards.
Pull the carpet off the tack strip in the corner of the room closest to the wrinkled section. To do this, grasp the corner of the carpet with pliers and pull it toward you. Keep pulling for several feet along both walls and fold the carpet back.
Adjust the depth of the teeth on the carpet stretcher by turning the screws on the spacer bar with a screwdriver. They should be long enough to bite into the carpet pile without penetrating the backing and coming in contact with the under padding. If they are too long, you might tear the under-padding.
Place the head of the stretcher face-down about a foot from the wall toward which you need to stretch the carpet, and anchor the foot against the baseboard on the other side of the room. Angle the stretcher slightly toward the corner of the room. Gently pull the handle on the stretcher to stretch the carpet.
Reposition the stretcher as needed to remove bubbles from the middle of the carpet. When the carpet is flat, use the knee-kicker to reset the carpet onto the tack strips.
Work your way from the middle of a wall toward the corner, positioning the head of the knee-kicker a few inches from the wall and pushing with your knee while you push the carpet under the baseboard and onto the tack strip with a stiff putty knife. When that wall is complete, reset the carpet on the perpendicular wall.