How did the US’ military help “the Allies” achieve victory?

The U.S. military provided help with strategic planning, but its greatest help was provided in other ways.
First, having the world's rising superpower on their side greatly increased the Allied countries' morale and stiffened their resolve. There was far less need to fear losing once the U.S. entered the war openly.
Second, the United States provided a huge amount of manpower to help fight the war, both in "boots on the ground" soldiers, but also the scientists exploring the latest in science and technology, such as splitting the atom to build the atom bomb, and the women back home who kept the factories running.
Finally, the United States' military could supply an almost endless supply of weapons. The country could and did turn its enormous industrial capacity to the war effort, churning out guns, bullets, bombs, tanks, planes, and battleships around the clock. Weapons help win a war, and with the assurance brought by U.S. supply lines, the Allies could turn from thinking defensively to planning offensives, such as invading Germany. The Allies knew at this point they could pound the Germans to smithereens because the U.S. (and the Soviets too, who had built up their industrial capacity) could provide the firepower. It might not always have been the most sophisticated weaponry, but it kept coming.