Truman's decision

Why did he order to drop the bomb? Did the Americans push him? And what has Russia to do with that all? Did he even have a choice?

Truman was under great pressure, from the public and from his advisors. And there was something else; and a lot of people don’t know about that. Truman didn’t see an end in the War with Japan and there weren’t enough forces to end the war fast. He was afraid, that the war would go too long. So he asked Joseph Stalin, the Soviet leader for help. Nevertheless these two countries hadn’t the best relationship with each other, they still agreed in working together. Because it would have positive affects for both of them. So Stalin promised to join the war against Japan on the 15th of August 1945.
But after Truman heard about the huge success of the Trinity test (atomic bomb test), his need for the help of the Soviet Union in the war against Japan was greatly diminished. If the Soviets would join the war, it would only invite them into the discussions regarding the postwar fate of Japan. So he told Stalin on July 24, 1945 that he has a “new weapon of unusual destructive force." And Stalin who knew about the American atomic bomb tests just answered: “make good use of it against the Japanese."
Only on day later on July 25th Truman decided to drop the bomb. They already discussed for month what cities should be attacked; there was Hiroshima, Kokura, Niigata, or Nagasaki as possible targets.
Then he told his forces, that they should attack the four cities on the list as soon after August 3rd as weather permitted. Targeting now simply depended on which city was not obscured by clouds on the day of attack.