I'm going to speak only to a specific role played by African-Americans during the war, namely pilots.

In 1940, there was a total of two African-American officers in the United states military, excluding chaplains. Col. Benjamin O. Davis, Sr. (promoted to Brig. Gen. late that year) and his son, Capt. O. Davis, Jr. (The elder can be seen awarding the younger a DFC in 1944 here). O. Davis Sr. was commissioned from the ranks, but Junior attended West Point, where he got the silent treatment for all four years.

In the fall of 1940, as you might know, the United States started to gear up for the possibility of war. The military was still segregated, and African-American units were led by white officers. There had already been pressure from the NAACP to open up the opportunity for African-Americans to join the Army Air Corps - which lead to the creation of black civilian training programs (sort of a precursor to the Civilian Air Patrol), and the rapid expansion of the military combined with advocacy from Eleanor Roosevelt herself led to the program's expansion and the creation of the 99th Pursuit Squadron. This was a HUGE deal. Not only because it meant that aviation was now open to African-Americans, but the implicit fact that the pilots would be officers. Being the only candidate for the position, O. Davis Jr. was put in command of the 99th PS, which was activated in late March of 1941.

Enlisted men began training as grounds-crew immediately, and the first class of 11 cadets and O. Davis, Jr. reported to the newly built Tuskegee Army Airfield in Alabama for pilot training. Amazingly, the resentment against this program was so high that the first Flight Surgeon to examine O. Davis, Jr. refused to certify him as fit for flight duties during his physical, despite the fact he clearly was. A second opinion had to be sought. During training, a number of white commanders oversaw the training. The first, Maj. Ellison ruffled local feathers by attempting to actually respect the African-Americans on the base, so was quietly reassigned despite being considered a very competent commander. Col. von Kimble was brought in, and immediately segregated the base facilities, and did nothing to advocate for the men about the foul treatment they received off base. Thankfully, cooler heads prevailed and he was replaced in turn by Maj. Noel Parrish who had previously been a flight instructor for the men, so had interacted with them a good deal and was well liked. He desegregated the base facilities, and made a point to interact with the black airmen as equals. Later on, he would be one of their most vocal advocates for assignment overseas.

Anyways, in July of 1942, the 99th Pursuit Squadron was at operational strength, and the 100th Fighter Squadron began to be trained. Due to racial politics though, the 99th remained in the US, with commanders hesitant to send them overseas. It wasn't for the better part of a year that they would ship out to North Africa in April of 1943. Looking back however, O. Davis would credit that year as a major boon to the airmen, as it allowed further training, and the building of a very close comradarie.

When they arrived in North Africa, they were to be mostly flying the P-40L, which they spent a few months training on. In May, they were attached to the 33rd Fighter Group, whose commander, Col. Momyer, was openly contemptuous of the black fliers, and wouldn't even return the salute of now Lt. Col. O. Davis, Jr. Momyer went out of his way to harm the 99th PS, and purposefully downplayed accomplishments in his reports after they entered combat on June 2nd.

Despite Momyer's attempts, the 99th proved themselves to be able to fly with any white squadron, even if it wasn't being communicated back to Washington. With the 100th FS being ready for combat soon, the 99th and 100th were combined into the 332nd fighter Group, to be commanded by Lt. Col. O. Davis, who returned to the US in 1943. Momyer's reports had called the black squadron's ability into question though, so whether the 99th would remain in theater was up in the air. Lt. Gen. Spaatz, who was deputy commander of the Mediterranean, wanted to see them gone, and reassigned to defending the rather unthreatened Panama Canal Zone. An Army inquiry was done, and Congressional Hearing was held, where O. Davis Jr. made a compelling case for his men, detailing the ongoing discrimination they had faced and how much they had done inspite of it. The Army's report on P-40 performance though sealed their fate, as it showed that they were well above the average for all squadrons equipped with the Warhawk. Numbers don't lie, as they say, and despite the best efforts of certain persons, the so-called "Tuskegee Airmen" were to stay in combat.

Eventually, four fighter squadrons would see action as part of the 332nd Fighter Group - the 99th, 100th, 301st, and 302nd - and while the 477th Bombardment Group was formed, it never saw action (due to the war ending). They would gain the nickname "Redtails" for the distinctive color scheme on their aircraft, and despite some people's assertions it isn't true that they never lost a bomber during an escort mission, they were still one of the absolute best records of any unit in the war, and were quite popular with Fifteenth Air Force bomber crews, (many of whom were quite surprised when they learned they were black airmen).

After the war, the program at Tuskegee continued for a few more years. In 1948, the US military was ordered to be desegregated. Lt. Col. O. Davis, Jr. was tasked with assisting the newly formed Air Force formulate a plan for integration. The stellar record of his men during the war, and their enduring reputation as some of the best combat pilots in the US meant that few squadrons would be upset to have them, and as such, the Air Force was the first military branch to fully integrate its units, with very little of the push-back seen in the Army, who took literally years to do the same.

Source: Aviation Elite Units 24: 332nd Fighter Group - Tuskegee Airmen