Though some integration of cafeterias and skating rinks and whatnot took place during the war, by and large the largest changes were in getting blacks in previously closed workforces. Many of these workplaces were still segregated, including the army, but the fact that Blacks were allowed into combat positions gave legitimacy to the desegregationists on the home front and laid the groundwork for the more intensive civil rights work of the 1960s.
At the start of the war, blacks were systematically excluded from many of the most desirable blue-color jobs, by both management and labor unions. As government orders became a substantial portion of factory orders, the federal government got leverage with which to change this. It may well be that FDR didn't care much about the plight of Blacks, and that others in the administration were outright racists, but Eleanor Roosevelt was outraged by the situation, and the general shortage of labor made the liberal quest to get blacks into the factories easily justifiable.
President Roosevelt was motivated by fear of public display and embarrassment, factors which would play into the hands of both his electoral opponents and, perhaps, the axis. Under threat of public demonstrations, he signed Executive Order 8802, integrating defense plants. This was later strengthened through further executive action, though Congress killed funding for the Fair Employment Practices Commission, which would have overseen the process.
Jobs were made available, though they were generally of the lowest grade manual labor. The government could not at that point mandate promotion by race.
Though this writeup discussed changes on the home front, a detailed history of the role of Black soldiers in the U.S. Army can be found in the official publications of the U.S. Army Center of Military History. Much of this is online at http://www.army.mil/cmh-pg/books/wwii/11-4/index.htm
from my homework for Historical Studies B-54 in November 1991.