A common phrase is "absolute power corrupts absolutely." How does Napoleon demonstrate this?
When first we encounter him, Napoleon is an out-and-out "pig of the pigs" (the swine equivalent of "a man of the people"). He champions the cause of the animal uprising, sings their anthems of rebellion, works in conjunction with his fellow creatures, and he assumes the role of the farm's de-facto leader upon their successful exile of the drunken and corrupt humans who once had treated them so poorly.
Soon after the animals gain control of the farm, they rename it "Animal Farm" in honor of their newfound liberation. Likewise, they codify a series of animal commandments, all of which decry the corruption of the humans regime while detailing their newfound equality amongst all four-legged friends. As they say: "two legs bad, four legs good."
Shortly after establishing the new order with Napoleon and Snowball as joint leaders of the farm, a series of mysterious events begins to unfold around Napoleon, and each of these serve as evidence to support the claim that he is slowly becoming drunk with power. The power shift starts innocuously enough as a litter of puppies is taken from their rightful mother and raised in a hidden loft under Napoleon's tutelage, and then a few extra buckets of milk go missing (later we learn that Napoleon had taken them to feed his growing army of attack dogs).
As the novel unfolds, Napoleon siezes every opportunity to strongarm his way into supreme commander status. In spite of Snowball's valliant performance at the Battle of the Cowshed, Napoleon unleashes his attack hounds and drives the heroic Snowball into exile.
Once Snowball has been exiled, Napoleon relishes in his supreme power, and uses it only to exploit the other animals and drive the farm further into poverty while he (and his innermost circle of pigs) grows fat and wealthy. Food rations are slashed, working hours are expanded, national anthems are banned, animal commandments are modified, and nay-saying animals who dare oppose Napoleon's regime are systematically executed so as to reinforce the pig's ultimate authority.
By the conclusion of the story, Napoleon has become the very embodiment of everything the animals once decried; he wears the same clothing that the humans once wore, he sleeps in their beds, he deals in the same financial transactions, and he drinks the same alcohol that he and all the other animals had once so vehemently opposed.