How were the first steps taken towards integration?(1945-1958)?
To me, the first major steps taken towards integration were legal ones -- they were law suits brought to try to tear down the idea of "separate but equal" as it applied to higher education. The NAACP felt that it would be better to attack segregation in higher education first and then work down to the high school and elementary school levels.
Two of the first victories in this effort came in 1950. In Sweatt v. Painter and McLaurin v. Oklahoma State Regents, the Supreme Court handed down decisions that hacked away at the idea that separate facilities could ever be equal. This line of reasoning led to the 1954 Brown decision.
Because of this connection, I see these 1950 cases as very important steps toward integration.
In addition to the above steps towards equality, I would say that some of the initial actions integrating our society were taken directly by the federal government in the form of Executive Orders issued by Presidents Roosevelt and Truman.
In large part due to the threat of a strike led by A. Philip Randolph, Roosevelt ordered equal pay be given to black workers in defense industries. While this did not directly cause us to be any more integrated than before, it was an important step in that direction.
President Truman was even more aggressive, and in 1948 he simply ordered the military to integrate, since he was the Commander-in-Chief. This meant he didn't have to go through a hostile and segregationist Congress.