In chapter one, Orwell has Old Major describe for the other animals on Mr. Jones's farm the vision he has of the animals throwing off the chains of human ownership and owning everything in common for the benefit of all. This is the vision of communism: no private property and the animals (proletariat) working for their own benefit, not to enrich a human (capitalist) like Mr. Jones.
What Orwell explores is how the dream turns into a nightmare, tracking how it happened in Soviet Russia through the allegory of Animal Farm. He attributes the transformation of Animal Farm into a totalitarian police state to the animals being too trusting and inattentive to how the ideals of the revolution are betrayed by the pigs. A slight twist of words or dropping of words or adding of words here and there utterly changes the meaning of the revolution. Further, as in the Soviet Union, leaders lied and betrayed the people and used a police state to keep the workers terrified. On Animal Farm, it is the dogs who enforce the rules of the pigs using violence. Orwell is saying that misusing the language, allowing too much power to amass in the hands of one or a few people, and allowing violence and terror to be unleashed on the citizenry undermined and ultimately destroyed any real communism, in the USSR or on the farm.
I think that the strongest detailing of Communism comes out through Napoleon. Orwell recognizes that Napoleon is the representation for Stalin, and his view of a Communist regime. When Napoleon runs Snowball off the farm, it is akin to Stalin running off Trotsky. As a result, the focus on Stalin as a leader and on Napoleon as a Stalin- like figure becomes central in Orwell's mind. Consider the purges that Stalin ordered and Napoleon's public "confessions." Another example is how Stalin ordered artists and musicians to construct and develop art that glorifies the state and overlooks all problems. Napoleon's use of Minimus in the same manner helps to bring this out on the farm. Finally, both Stalin and Napoleon are experts in using propaganda to manipulate situations to their own benefit. They demonstrate how figures can lie and liars can use figures in order to substantiate their own understanding of how reality should be constructed. In doing so, their use of propaganda serves to bolster their own leadership and political control over their people, who are powerless to stop an onslaught of repressive government. In constructing Napoleon in the manner he did, Orwell offers the most stinging of critiques against Russian style Communism.