The United States and Britain never trusted the Soviet Union, even during the war. But they cooperated in order to fight the common enemy, the Nazis. Though after the war, the US and Britain gave sanctuary to a lot of former Nazis, because they had intelligence information on the Russians. The US began to mobilize their military, in order to meet what they perceived as a Russian threat to Europe.
On the Russian side, after losing 28 million people in a war that devastated their nations infrastructure and population, they were determined never to let that happen again. With the US and Britain giving sanctuary to former Nazi scientists and intelligence officers, and gearing up their militarily assets to possibly fight them in East Germany, the Russians decided to meet the threat.
The US spread a lot of propaganda about the Soviet Union, that they wanted to crush the "free world" and bring about a global Communist society. In reality, Russia was content to live within their borders using Eastern Europe as a buffer zone against the West, which had in the past killed millions of their people.
Why did the Soviet Union occupy Eastern Europe? A lot of those countries, like Hungary and Romania fought alongside the Nazis against them. Also if war was going to come again, Russia did not want it to take place on its soil. Better to turn Eastern Europe into the battleground rather than have the enemy pushing towards Moscow and laying siege to St. Petersburg, which happened in WWII.
Misunderstanding, misconceptions and propaganda all led to the Cold War. Also the fact that the US and Britain had no sympathy, compassion or respect for the sacrifice of the 28 million Russians who died saving the world from Nazism. That was the saddest chapter in the whole mess called the Cold War.