Depending on the type of leather, most coats can be cleaned using a soft soap, warm water and a rag. If the coat is suede, don't attempt to clean it at home. Take it to a professional cleaner.
For most leathers, much of the dirt can be wiped off using a rag. If the coat has tougher stains or dirt spots, mix a bowl of warm water with a soft soap. Hand soap or baby shampoo is best when cleaning leather. Dip a clean rag into the bowl of soap solution and gently rub it over the surface of the coat. The soap should work itself into a lather. If it doesn't, there is too much water in the solution. Spend the most time on the spots with dirt, but be sure to cover the whole of the coat to clean off all the dirt. After using the soap, rinse the coat with cool water either directly from a faucet or using a new rag with only water on it. After cleaning, apply oil onto the coat. The best option is mink oil, but olive oil also works. Gently rub a small amount of oil onto the surface, removing any excess oil. If the coat shines, too much oil was used. The oil prevents the leather from drying or cracking.