As with so many other questions, the answer to this question would depend largely on which historian you asked. But there are a few points on which I think most would agree. First, the Grand Alliance had never been terrible cozy to begin with, as Stalin was well aware of Anglo-American antipathy toward his regime. The Americans and British, on the other hand, didn't trust Stalin, largely due to his duplicity in the Nazi-Soviet non-agression pact of 1939.
In short, though, the Cold War emerged from disagreements about what post-war Europe, and indeed the world, would look like. At the Yalta Conference, Stalin gave assurances that he would allow democratic elections in Poland. By the time of the Potsdam Conference, new president Harry Truman was convinced that this was not happening, and took a hard line in promoting United States interests. He was particularly emboldened by the fact that the Americans were in possession of the atomic bomb, which he used shortly thereafter to end the war in Japan.
In the wake of the war Stalin determined to create a buffer zone of friendly states on his western flank. He thus installed communist regimes in Poland, Romania, and other eastern European nations, actions that the Truman Administration viewed as aggressive. Diplomat George Kennan's "Long Telegram" convinced American policy-makers to take a hard line on the matter (hence the "Truman Doctrine" of containment) and when communist revolutions appeared imminent in the rest of Europe, the US instituted the Marshall Plan, which flooded Europe with billions of dollars in investment. The Soviets viewed this as economic imperialism. By 1948, China was in the midst of a communist takeover, and Europe was divided among states supported by the US and Soviets. This was the beginning of the Cold War.