How and why was it brought to the Supreme Court

In 1951, a class action suit was filed against the Board of Education of the City of Topeka, Kansas in the United States District Court for the District of Kansas.  The National Association for the Advancement of Colored People recruited thirteen angry parents who were the plaintiffs who asked that their school district to reverse its policy of racial segregation.  Separate elementary schools were operated by the Topeka Board of Education under an 1879 Kansas law, which allowed districts to maintain separate elementary schools facilities for black and white students.  

The District Court ruled in favor of the Board of Education, saying that the U.S. Supreme Court precedent set in Plessy v. Ferguson, 163 U.S. 537 (1896), which had upheld a state law requiring "separate but equal" segregated facilities for blacks and whites in railway cars.  The three-judge District Court panel agreed that segregation in public education had a negative effect on black children, but said that black and white schools in Topeka were substantially equal with respect to buildings, transportation, curricular, and educational qualifications of teachers.  This case was appealed to the Supreme Court.