Basically the title. How did it spread You had countries across the globe with their own governments and systems.
So how did communism expand from the Soviets to other places across the globe? Were people from Russia walking to government leaders and telling them "hey you guys should run your country like this because it's much cooler".
The same question can be asked for capitalism too, but I just figured at that point the USA or their allies funded groups to revolt communism. I guess it depends on which happened first.
But point is, I'm trying to picture in my mind how someone from Soviet Union went to Africa, the Middle East or South East Asia and told them how to run their country. I'm also trying to picture in my mind how these people from these countries literally killed each other in civil war over communism and capitalism.
Like why couldn't they just say "screw you guys we run our country like we want to".
Although the whole world and 80 years of the Soviet Union is a broad topic to cover, generally the USSR supported and directed local homegrown movements via the Comintern. Socialist/Communist ideas had been spreading around the world for 70 years prior to the October Revolution in Russia: Marx's "Communist Manifesto" was published in 1848. Subsequently, the International Workingmen's Association, later called the First International, was formed in 1864 as an international conference of left-wing parties across the world. This was succeeded by the 2nd & 3rd internationals, with the third being renamed the "Comintern" and directed formally by the Soviet Union to support socialist/communist parties across the world. Different parties in a given country would compete for official recognition in the Comintern, which would bolster their resources and raise their profile. For example, John Reed from the American Communist Labor Party of America went to Russia in 1919 to seek Soviet recognition of the CLP as the "official" party in America.
The local party which won Comintern support would then take a party line directed from Moscow, usually focused on the Soviet Union's foreign policy goals rather than local conditions. This discrepancy is discussed in Arthur Koestler's contribution to "The God That Failed", describing his time in the 1930s KPD (Communist Party of Germany): "I may have been somewhat bewildered when we were told by the instructor that the Party's main slogan in the coming elections to the Prussian Diet was to be not the seven million German unemployed, or the threats of the Brownshirts, but 'the defense of the Chinese proletariat against the aggression of the Japanese pirates.'"
European colonial empires exposed their subject to western left-wing politics. Once again, the whole world is a big subject to cover, but to give one brief example of how the Communist Party came to power in Vietnam, Ho Chi Minh became interested in left-wing politics in the post-WW1 era while living in France, he became a member of the French Communist Party and participated in congresses of the Third International. After receiving further education and training in the Soviet Union he went to Asia and founded the Communist Party of Vietnam.
Sources: The God That Failed (1950) ed. Richard Crossman