It's a very broad question, and pretty difficult to answer in a discussion post. You'll want to start in the early 1950s with Jim Crow segregation laws, the murder of Emmitt Till and the court decisions Brown vs. Board of Education. The Civil Rights Movement is commonly viewed to have started then, and lasted through Martin Luther King's assassination in 1968.
I think that you have already found out that there are some very quality thinkers who can post thoughts to your question. You will need to enhance this by focusing your thoughts and questions to a particular topic. There are many elements to the Civil Rights Movement that can be answered and addressed. Being able to identify these elements out and ensuring that there is some level of focus can reveal many strong and divergent thoughts on a topic as powerful as the Civil Rights Movement on political, social, economic, and psychological levels. The idea of a group of people appealing for their basic rights and then how this expands into different areas of American historical and political thought is powerful. The sociological implications are still felt today and in focusing a question along these lines, you will be able to partake in a dialogue that has helped allow America to fulfill one of its greatest promises as a nation of free and dynamic discourse.
It 1948, President Truman signed an Executive order:
"It is hereby declared to be the policy of the President that there shall be equality of treatment and opportunity for all persons in the armed services without regard to race, color, religion, or national origin."
During this time period there was a lot of discrimination and segregation. Blacks and whites were still not equals. For example, blacks sat in the backs of buses, attended different schools, etc. America was very segregated.
In 1955, a man named Emmitt Till, was brutally murdered for supposedly whistling at a white woman. Two white men were acquitted by a white jury and bragged about the murder later. That same year a woman named Rosa Parks refused to give up her seat on the bus to a white person. This caused a lot of outrage. This is when the Montgomery Bus Boycott occurred. The next year buses were desegregated.
In 1964, President Johnson signed the Civil Rights Act of 1964 which prohibited discrimination based on sex, color, religion, or national origin.
In 1968 Martin Luther King was shot to death by James Earl Ray.
These are just a few of the things that occurred. There is so much more.
It would really help if you would ask a more specific question since whole books have been written on this subject.
You can say that the most famous part of the Civil Rights Movement started with the Montgomery Bus Boycott in 1955-6. This is the one that was started by Rosa Parks.
The next famous incident was the sit-ins and the lunch counter in Greensboro, NC by college students.
The most famous person involved in the movement was Martin Luther King, Jr.
The movement achieved its first set of goals when the 1964 Civil Rights Act was passed, banning discrimination in public accommodations.
Civil rights are the freedoms and rights a person is entitled to a member of a society. These include rights such as freedom of speech, of the press, and of religion, right to own property, and to receive fair and equal treatment from government, other persons, and private groups. Civil rights are guaranteed under the constitutions of many countries. All civil rights have limits, Civil rights do not extend to actions of individuals that might harm the health, welfare, safety, or morals of others, or interfere with rights of others.
The United Nations General Assembly adopted a Universal Declaration of Human Rights in 1948. It states that all people are born free and are equal in dignity and rights.
Though civil right are supposed to be something a person is supposed have naturally by birth, in the past most of the countries, typically ruled by monarchies, put severe restrictions on civil rights. The concept and practice of guaranteeing basic rights and freedoms to individuals became popular as countries adopted democratic form of government with clearly defined constitutions. But even in democracies the civil rights of some sections people were severely restricted by various discriminatory practices based on race, gender, economic power, and similar considerations. People in many countries had to struggle to secure civil rights for all sections of society.
One of the most difficult civil rights movement took place in the United States for rights of black Americans. These people campaigned for equal rights from the 1800's. onward. This fight for civil rights became a major movement during the 1950's and 1960's, and led to enacting of important civil rights legislation to end discrimination against black Americans.
Ever since end of slavery after American Civil War, blacks in both the North and South had faced discrimination in all walks of life. Initially the black Americans were too weak economically, and lacked the will to struggle for equality against heavy odds piled up against them. But gradually their strength and aspiration developed and a movement for civil rights developed gradually.
The movement became much more powerful after the Second World War. Campaigning and other actions of civil rights leaders resulted in several Supreme Court decisions declaring many discriminatory practices illegal. For example in 1954 the court ruled that compulsory segregation in state schools was illegal.
In 1955, Martin Luther King, Jr. (1929-1968), who became one of the major leader champion of civil rights, began organizing protests against discrimination. He was able to inspire blacks as well as whites for achievement of equality for all. He won the 1964 Nobel Peace Prize for leading nonviolent civil rights demonstrations.
Under the leadership of Martin Luther King, Jr. the civil rights movement won wide support among whites, and laws that had barred integration in the Southern States were abolished.
Equal civil rights became the major issue during the Kennedy administration. In response to this Kennedy asked Congress to pass many legislation restricting discriminatory practices. This resulted in passing of Civil Rights Bill that Kennedy and his successor, President Lyndon B. Johnson, had recommended. The Civil Rights Act of 1964 prohibited racial discrimination in public places and called for equal opportunity in employment and education.
It was aimed at outlawing racial discrimination against African Americans through 1955 to 1968.