Use the garment brush to brush over the coat well to remove any visible dust and particles. It also loosens up any sticky stains.
Clean the bathroom sink and fill it with cold water. Do not use hot water because it can damage the fabric and loosen it. Pour a cup of wool friendly detergent into the sink and make it soapy. Now dip the coat into it.
Wear gloves to protect your hands and wash the coat under the soapy water. Remove all stains. Take out the coat and place into a drain basket. Use your hands to drain out as much water as possible through pressing. Do not wring at any cost. It will deform your coat.
Drain the soap water from the sink and fill it again with clean cold water. Dip the jacket into it and rinse, to take off all the soap. Repeat with fresh water if needed to get rid of all the soap.
Place on a drying rack and air dry. Flip over a few times to ensure that the coat has dried all over. It might take a couple of days. Use an iron with a steamer feature to soothe down the wrinkles and bring back the coat in shape.
If you want to machine wash, fill the washing machine with cold water and washing detergent. Thoroughly mix in the detergent. Put the coat into a mesh case and lower into the machine. The mesh case will prevent it from getting deshaped by the spin cycle. Wash on a slow spin cycle. Dab the coat dry with a clean towel. Place on a hanger and let it dry before using.