Mix 1 part distilled white vinegar and 2 parts neat’s-foot oil together in a large bowl. Pet supply stores and hardware stores both sell the oil. According to Mrs. Clean, food-grade linseed oil is a suitable replacement for the neat’s-foot oil.
Wipe the couch down with a microfiber cloth. The cloth is soft enough that it will not scratch or otherwise damage the leather. The cloth should also absorb and pull off any debris stuck to the leather, including dust and dirt.
Clean the couch with the distilled white vinegar mixture. Dip one of the cloths into the mixture and squeeze out most of the liquid. Rub the cloth over the couch, dipping it back into the liquid as needed. Once you finish wiping down the couch, wipe the leather with a dry cloth that removes any liquid.
Turn the hairdryer on a low setting and hold at least six inches from the leather. Gently move the hairdryer back and forth across the leather. Turn the heat up if the wrinkles still appear. Keep moving the hairdryer across the leather until you no longer see the wrinkles.
Tear the paper grocery bag in half and press one piece of the bag against any remaining wrinkles. Turn the iron on its lowest setting and press against the paper bag. Move the iron across the paper, gently pressing down. Keep moving the iron over the bag until the remaining wrinkles disappear.