First, you need to be clear about what type of leather you are dealing with, if your jacket/vest is suede or nubuck you should take it to a specialist cleaner. A leather piece should never be totally immersed in water or placed in a washing machine. Regular conditioning and wiping with a damp cloth will help prevent a build-up of dirt and grease and storing your jacket in dry conditions will prevent mould.  To remove dirt and grease or light staining, use a damp cloth and soapy water.  Blot rather than rub and avoid over-wetting the leather. Dry the leather naturally but do not allow it to remain damp for long.