Lay out the rug in the sunlight all day, if the rug is not too wrinkled. The heat of the sun will naturally remove the wrinkles.
Place some heavy items on the wrinkled portions of the rug. This could be furniture, a stack of books or anything heavy enough to reduce the wrinkles. Leave the items on the rug overnight and check for wrinkles the next day.
Iron the wrinkles. Iron the rug on a low heat setting and make sure you are ironing with the nap of the rug, not against it.
Place a hair dryer on the back of the rug where the wrinkles are and heat the rug until the wrinkles are gone.