After World War II, the communists, led by Mao Zedong had many advantages. They controlled the important areas of eastern China and around a quarter of the land.  A very important strategy that Mao Zedong utilized was to win favor with the peasants, which were an overwhelming majority of the population.  He promised that he would create reforms that would improve their lives.  For this reason, Mao was extremely popular.  Unemployment and other economic difficulties in Nationalist-controlled areas were making their leader, Chiang Kai-Shek equally unpopular.   So with popular sentiment on the side of Mao, he planned and coordinated a very cautious strategy to win the war.  He would concede land to the nationalists in instances where his forces were outnumbered.  In this way, he was able to preserve the number of troops fighting for him rather than wasting them in battles they could not win.  Support, in the form of weapons from the Soviet Union, was also an important advantage that Mao had.  Much of the financial support that Chiang Kai-Shek and the Nationalists received was wasted through corruption and mismanagement.  

How did the Chinese Communist Party take control of China?

The Chinese Communist Party took control of China by winning a long civil war.  This war can be said to have started in 1927.  It ended in 1949 when the communists, led by Mao Zedong, finally defeated the Kuomintang, who fled to Taiwan.  There was a pause in the war during World War II.  During that time, the communists and the nationalists both worked together (though  with the Americans to oppose the Japanese who had invaded China in the late 1930s.  However, once the Japanese were defeated, the Chinese factions took up fighting with one another again.