explain the events leading up to the brown v. board of education decision and summarize the supreme court's ruling

Short answer:

Plessy v. Ferguson (1896) was a Supreme Court decision that upheld the principle of "separate but equal" in regard to racial segregation of railroad transportation.

After that decision, the "separate but equal" principle was applied to other areas, such as education.

Brown v. Board of Education (1954) challenged the "separate but equal" principle in regard to segregation in education. The Supreme Court overruled the previous decision. Racial segregation was declared to be inherently unequal and unconstitutional.

More details:

In the decades after the Civil War, states in the South began to pass laws that sought to keep white and black society separate. In the 1880s, a number of state legislatures began to pass laws requiring railroads to provide separate cars for passengers who were black. At the heart of the case that became Plessy v. Ferguson was an 1890 law passed in Louisiana in 1890 that required railroads to provide "separate railway carriages for the white and colored races."

In 1892, Homer Plessy, who was 1/8 black, bought a first class train railroad ticket, took a seat in the whites only section, and then informed the conductor that he was part black. He was removed from the train and jailed. He argued for his civil rights before Judge John Howard Ferguson and was found guilty. His case went all the way to the Supreme Court which at that time upheld the idea of "separate but equal" facilities.

Several decades later, the 1896 Plessy v. Ferguson decision was overturned. Brown v. Board of Education, decided by the US Supreme Court in 1954, extended civil liberties to all Americans in regard to access to education. The "separate but equal" principle of Plessy v. Ferguson had been applied to education as it had been to transportation. In Topeka, Kansas, Oliver Brown filed a lawsuit after the public school district refused to enroll his daughter in the school closest to their home, making her instead take a bus to a blacks-only school. Other families joined the Brown family lawsuit. When it went to the level of the Supreme Court, there were other cases from other parts of the country that the Supreme Court combined with it. The full name of the case at the Supreme Court level was Oliver Brown, et al. v. Board of Education of Topeka, et al. The arguments were heard before the Supreme Court in 1952 and 1953, and the Brown v. Board of Education decision was issued in 1954. The standard of "separate but equal" was challenged and defeated. Segregation was shown to create inequality, and the Supreme Court unanimously ruled segregation to be unconstitutional.