The Tuskegee Airmen fought in the African and Italian Campaigns, along with fighting in Europe. In Africa, Italy, and Europe they dealt with the Luftwaffe, Nazi Germany's elite air force. In Africa, they would bomb the Afrika Korps' air bases and troop bases. The Afrika Korps were led by Field Marshal Erwin Rommel. The fighting took place in Northern Africa, as seen in the map below. Whether they were bombing Nazi bases or fighting the Luftwaffe, they were busy flying and fighting.
In Italy, they essentially performed the same operations. During Operation Husky, which was when American and British soldiers attacked Sicily, they bombed the shores and more inland for the infantry and tanks to move through without too much of a struggle. The Italians and Nazis had troops and aircraft here. From Sicily, they would move up into Italy and up through the country.
Once they were through with Italy and Africa, they would prep for D-day, perhaps the greatest aquatic invasion in history. The Tuskegee Airmen's role in D-day started early in the morning, when they traveled over Normandy, dropping thousands of bombs. This was to weaken the Nazis fortifications. They also would drop paratroopers behind enemy lines to weaken the Nazi troops that weren't shelled as hard. The reason you hear that Omaha Beach was so brutal was because many of the bombs that were aimed for it were off target, hitting very close, but not close enough. After D-day, they began to bomb and attack German cities such as Berlin. The Luftwaffe became even more brutal then ever. This was the aerial front that lost the most men. After the war in Europe was over, some of the Tuskegee Airmen helped in the Pacific theater. Then, they returned to home to battle even more racism.
Top to Bottom: Picture of Europe, Picture of Italy and Sicily, and Picture of Northern Africa.