It is stated that not one Supreme Court Case alone ended the segregation. There are dozens and dozens of cases that were run through the Supreme Courts that regarded segregation. Each one took part in ending segregation all together.
De facto and illegal examples of segregation have not ended and will not end unless people decide to end them. Legal segregation had virtually ended under Eisenhower, but Kennedy did what he could to enforce federal laws against segregation.
There is no exact date that segregation began, because since America was "founded" there has always been segregation. Segregation has always had a prevalence in America from the time of slavery to the days of separate restaurants and bathrooms. The year that segregation ended was 1967.
In the state of Alabama, segregation ended on November 13th, 1956. In June of the same year, it was ruled by the federal district court that the segregation ordinances in the city of Montgomery, were unconstitutional.
I'm not sure, but 'Brown Vs. The Board of Education ended racial segregation in public schools. Brown fought this case because he didn't want his daughter to have to walk 2+ miles to school everyday, alone. He eventually won, and the supreme court ruled against racial segregation in schools.
Black soldiers who returned from Europe after World War I were the first large group to agitate against segregation. The Civil Rights Act in 1964 and the Voting Rights Act in 1965 legally ended segregation.