During the 1950s and early 1960s, African American activists used two main tactics. In general, the tactics were used somewhat sequentially, not at the same time.
The first tactic to be used was litigation. The NAACP’s legal defense fund conducted a program of litigation that was meant to get the doctrine of “separate but equal,” set out in the 1896 case of Plessy v. Ferguson, overturned by the Supreme Court. The NAACP chipped away at the doctrine and managed to get it completely overturned (at least in the area of public education) in the Brown v. Board of Education decision of 1954.
The second tactic was nonviolent civil disobedience and direct protest. This tactic was started to some degree in the Montgomery Bus Boycott. It then escalated with the sit-ins that began in Greensboro, North Carolina in 1960. From there, this tactic became the staple of the Civil Rights Movement. It culminated with such things as the marches for voting rights in Alabama and the March on Washington. Throughout this time, the main leader of the movement was Martin Luther King, Jr., who is most closely associated with these tactics.
A third tactic was violent protest and calls for armed revolution by activist individuals and groups like Malcolm X and the Black Panthers.