There can be many different answers to this question. I would suggest that President Johnson's Great Society initiatives are amongst some of the most effective in fighting poverty. President Johnson's Great Society policies were effective because it acknowledged the concept of poverty in American life. Johnson was explicit in suggesting that combatting poverty was an essential tenet to American identity: "And with your courage and with your compassion and your desire, we will build a Great Society. It is a Society where no child will go unfed, and no youngster will go unschooled." Johnson has to receive credit for making the war on poverty an essential part of his administration. Poverty was not something to be hidden and a source of shame in the nation. Rather, its presence was meant to cause shame in Americans and galvanize them into action. His employment of "courage" and "compassion" in fighting poverty helped to create policies that attacked social, political, and economic disenfranchisement in American society. Poverty and lack of opportunity were not elements to be tacitly accepted. Johnson constructed a focus in which Americans recognized the need to look at what is and transform it into what could be. The "unconditional war on poverty" represented executive power being marshaled against economic and social disenfranchisement.
Given how administrations before and after Johnson's never really openly acknowledged poverty in the way his did, I would argue that this focus itself was one of the most effective in fighting poverty. Enabling children to participate in Head Start, helping children to attend higher education through federal programs, and establishing Medicare are policies that directly aim in fighting poverty. Programs like these make it official that poverty was something to be eradicated and not something to be accepted in American life.
The Great Society initiatives have its detractors and there could be follow up answers that easily challenge this one. Yet, I think that Johnson's direct attack on poverty and legislation that sought to address poverty makes his administration a significant and effective force in fighting poverty. It has been argued that "from 1963 when Lyndon Johnson took office until 1970 as the impact of his Great Society programs were felt, the portion of Americans living below the poverty line dropped from 22.2 percent to 12.6 percent, the most dramatic decline over such a brief period in this century." This can be used as an argument to demonstrate how the Johnson Administration constructed effective policies in the war on poverty. In a nation that still struggles with the very issue of poverty today, one recognizes how radical and forward thinking President Johnson's approach to poverty was and how his administration was one of too few that sadly acknowledged the presence of and the desire to end impoverished conditions throughout America.