The manufacturing of all of the materiel needed for World War II was funded in two main ways. These were taxes and borrowing.
Obviously, the war was tremendously expensive. However, there was a great deal of room to raise taxes in those days. The pre-war income tax rate had been 6%. In 1942, tax rates were raised by a tremendous amount, with the top marginal tax rate being set at 88%. This, of course, raised a great deal of money that could be used to help pay for the war. However, the government was still spending much more than it could raise in taxes. This meant that the government also had to borrow a great deal of money. Fortunately, Americans had a fairly large amount of money saved in those days. Also, during the war, there was little for them to buy as many things were rationed. These factors, combined with intense patriotism, allowed the government to borrow huge sums of money by selling war bonds.
So, the US paid for this war by taxing and by borrowing. It was in a position to do so because its taxes had been low and there were excess savings that the government could borrow.