Fill the steamer with water to the correct level, as indicated by your particular steamer. Plug the steamer in and allow it to warm up.
Hang the rug in a place where you will be able to easily reach it; steaming tends to be more efficient when the item is hanging rather than lying on the floor.
Position the steamer nozzle about three to six inches away from the rug. Slowly move the steamer nozzle over the wrinkled areas of the rug. Move the nozzle up and down over the afflicted areas rather than holding it in one spot, which can cause the rub to burn.
Allow the Aubusson rug to dry completely before rehanging in its original spot.
Plug your iron in and turn it to a medium heat setting.
Drape the Aubusson rug over an ironing board, back side up. Carefully iron the back of the rug; keep the iron continuously moving up and down over the fabric to avoid burning any one particular spot.
Flip the rug over to see if the front still contains any wrinkles. If it does, place a thin cloth between the rug and iron so that the heat from the iron does not damage the antique thread used to create the rug's design, and iron the area.