Final answer:
The most effective methods in the 1960s civil rights movement were non-violent civil disobedience and economic boycotts, led by figures like Martin Luther King Jr., and resulting in significant legal and societal changes.
Step-by-step explanation:
In the context of the 1960s civil rights movement, the most effective method for bringing about change was through non-violent civil disobedience and economic boycotts. Important figures like Martin Luther King Jr., who led the Southern Christian Leadership Conference (SCLC), significantly contributed to this approach, advocating for peaceful protests and boycotts. One of the hallmark events demonstrating the efficacy of non-violent civil disobedience was the Montgomery Bus Boycott, sparked by Rosa Parks' refusal to give up her seat, leading to a Supreme Court ruling that segregation on public buses was unconstitutional. Other key activities included sit-ins at lunch counters, the Selma to Montgomery marches, and the iconic March on Washington. These nonviolent actions produced crisis situations that necessitated immediate responses from authorities and highlighted the injustices faced by African Americans, thus pushing forward the civil rights agenda.