How does theoretical communism relate to Animal Farm?

Theoretical communism relates to Animal Farm in two ways. First, it appears in Old Major's vision of a farm run by the animals before they chase Mr. Jones off. He tells the animals that their troubles are caused by mankind exploiting them and taking the fruits of their labor while doing little or no hard work themselves. If the animals could get rid of man, they could enjoy the profits of their labors themselves and live freer and more prosperous lives. This parallels the writings of communism in the nineteenth century, before there had been a successful communist revolution, telling working class people that if they got rid of the bourgeoisie (what we would call the one percenters today), they could have freer and more prosperous lives.
Old Major also tells the animals never to compromise with mankind, which parallels the communists saying never to compromise with the bourgeoisie:

Never listen when they tell you that Man and the animals have a common interest, that the prosperity of the one is the prosperity of the others. It is all lies. Man serves the interests of no creature except himself.

Second, after the rebellion, when the animals expel Mr. Jones and his men, for a short time, they experience giddy happiness and they (with a few exceptions, like Molly) work hard together, each according to his ability, to bring in the harvest. This is similar to the early years after the Russian Revolution, before the communist project was corrupted into totalitarianism, when some of the people whole-heartedly worked to implement communist principles.