How does Napoleon gain power over Animal Farm and how does he maintain it?

Napoleon gains power over the animals by two means. First, he twists the ideas of the animals' revolution to suggest that questioning his authority is tantamount to treason to Animal Farm, and the good of the whole. This is part of his larger strategy of manipulation of the truth. Squealer, his "propaganda minister," is especially adept at getting the animals to believe whatever is necessary to promote Napoleon's power. After Napoleon drives Snowball from the farm, for example, it is Squealer who convinces the animals that constructing the windmill was actually Napoleon's idea (even though Snowball had publicly endorsed it against Napoleon's wishes). He further suggests that Snowball, who had in fact fought bravely in the battles to establish Animal Farm, had in fact been in league with Jones, the farmer, the whole time. Snowball's ability to twist information is best exemplified by the winnowing down of the original Seven Commandments to one, which claims that while all animals are equal, some animals "are more equal than others."

The other means by which Napoleon maintains power is terror. We see this most clearly when he uses the dogs to massacre dozens of animals in the barnyard, each of which is accused of (indeed many freely confess to) treason against the farm. This bloodletting is meant to remind readers of the bloody purges of Joseph Stalin in the Soviet Union. Like Stalin and many other dictators, Napoleon justifies this violence by suggesting that it is all for the greater good, but also that the farm is constantly under threat from the outside. The humans, Napoleon claims, are conniving with Snowball to destroy the animals' ideal society. If the farm is always in crisis, then Napoleon can always justify extreme means to supposedly protect it.