Mao Zedong and Fidel Castro both came to power when their countries were economically depressed and politically unstable.
Mao Zedong came to power in 1949 after a standoff between nationalist and communist forces in the wake of World War II. He successfully led a cultural revolution for China, inspired by his Marxist views and his study of the Russian Revolution when working as a librarian's assistant as a young adult. Mao was ultimately successful insofar as he created the People's Republic of China; however, it was not an especially just or prosperous regime. Nevertheless, he put China on the map as a major communist power, distinct from the Soviet Union.
Zedong was aided by a group called the Red Guards—young proponents of his philosophy (often students) who sought to rid China of its old culture, customs, ideas, and habits. This group shared Mao's vision for a Cultural Revolution in China, though the Red Cards wreaked havoc on China by seeking to brutally stamp out an entire tradition.
Castro came to power in Cuba as a dictator after leading a coup against Fulgencio Batista. In the 1950s, Castro resorted to guerrilla warfare, leading to a period of prolonged violence in Cuba. Though conditions in Cuba have improved since Castro, communism left many Cubans living in poverty despite Mao's promotion of a Marxist-inspired communist ideology that attracted many Cubans. Though his aims and tactics were questionable to say the least, Castro was so successful at fostering an ideology that promoted guerrilla warfare that the United States tried to assassinate him, undertaking the infamous Bay of Pigs invasion, wherein CIA trained Cuban exiles to fight against Castro's guerrilla fighters in an expedition that failed miserably.
Some political scientists (especially with the luxury of hindsight) argue that the communist revolutions—begun in China in 1949 and in Cuba in 1959 used communism as a convenient banner for revolutionary activity, but in effect acted only to propel the eventual emergence of state-level capitalism.