Toss the coat in the dryer along with a fabric-softener sheet, and air dry for about 20 minutes. Then run hot water in the bathtub, make sure to leave the drain open, and close the door until the bathroom gets fairly steamy. Hang the coat in the steamy bath for about five minutes. A handheld steamer will also work. Finally, rub the coat with a dry sponge or fabric brush.
Wooden hangers are perfect for a heavy wool or leather coat.
Raincoats may lose some of their ability to shed water after a trip to the dry cleaners. Ask for a water-repellency treatment each time the coat gets cleaned. Spot clean leather or leather-like coats with a sudsy sponge, but don't use solvents or shoe cleaners. Oil soap may be used, but mix with water according to the label directions. Genuine leather needs professional cleaning by a specialist.