Reconciliation of Past Sins

If a person has murdered someone: ie. A fellow human being (eg. By directly attacking someone; or by indirect attack- by speech/action ; or by other means such as abortion) , what methods are available for such a person for personal reconciliation? It is inevitable that the Law of Karma is in direct effect, but how can such a person attain peace of mind and repay for his sins truly? Many patients I meet in surgery wards have serious past histories of attacking/assaulting others and murder is inevitable sometimes. Please offer your advice. It will greatly help me when consoling such persons in the future. Thank You!