Blame is the assignment of responsibility from one entity to another. Blaming is the action of assigning this blame to another, often from oneself. These activities seem basic to hominid behaviour, as the infamous cat did it incident with Koko the Gorilla demonstrated very vividly.
Blaming is nearly universally observed in children. It seems to be an essential part of human development. When language skills develop, one of the first practical things that can be done with them is to apply them to blame others for one's own misdeeds, and get them sanctioned or punished while one simply continues to engage in more of same.
Lying is often involved in blaming, although of course it is possible to assign blame to someone using truth perhaps however selectively applied. For example, someone could be correctly blamed for hitting someone else, and charged with assault, but the motivation, say a prior assault by the individual claiming harm, might be concealed. Thus the scope of time and events and interactions considered is a pre-requisite to any assigning of blame.
Some systems theorists and management consultants, such as Gerald Weinberg, held that the flow of blame in an organization was itself one of the most important indicators of that organization's robustness and integrity. Blame flowing upwards in a hierarchy, he argued, proved that superiors were willing to take full responsibility for their orders to their inferiors and supplying them with the resources required to do their jobs. But blame flowing downwards, from management to staff, or laterally between professionals, were signs of organizational failure.
Healthy organizations had means, such as formal disapproval, censure and demotion, that they can apply to managers and leaders who do not take full responsibility for their actions - in effect, to blame them for deflecting blame, rather than admit and redress it. These measures are quite common in government and diplomacy, in situations where no punishment can be applied, e.g. due to diplomatic immunity.
Resignation of a public official is another common way to accept blame.