The Cold War was not a single way but rather a collection of wars that were fought in the wake of the Second World War amid the high tensions that continued after the defeat of Germany and the other Axis. There is no definite start date but the end of the Second World War is a good indicator, though some believe it started later, and it finished in 1991 with the collapse of the Berlin Wall and the eradication of the Soviet Union.
First, let us address the terminology. It is called the Cold War because there was very little combat, especially in Europe, but lots of tensions. In this sense, the feeling between different countries of the world can be considered cold.
The main point of friction throughout the period of the Cold War was essentially between the West (mainly the United States) and the East (the Soviet Union). For much of the conflict, Germany was the epicentre of the Cold War. After the Second World War, there was a vacuum of power in the country and this was filled partly by the US, the UK and France (the West) and partly by the Soviet Union (the East). The Soviets dominated much of Eastern Europe including Poland, Estonia, and Hungry.
However, the conflicts in the Cold War spread much further than Europe. There were many proxy wars that were fought across the world, the ideology of capitalism versus communism been constantly contested. Some examples of this are the Vietnam War and the Afghanistan war. That is the Afghan war in the 1970’s and not the recent one which involved America.
The Cold War ended when the Berlin Wall came down and the Soviet Union collapsed. Reunification of Germany followed along with many other countries gaining their independence from the Soviets.