Napoleon has two main methods to keep the others animals from revolting, both of which mirror the ways dictators in real life hold onto their power.
The first is the threat of violence. While the other animals aren't paying attention, Napoleon goes off with a group of puppies and trains them to protect and be loyal to him alone. By the time they grow up, they are violent and menacing animals.
They make their first appearance in a terrifying way: "nine enormous dogs wearing brass-studded collars came bounding into the barn." They chase off Snowball. They then guard Napoleon as he announces that the pigs will from now on make the decisions about the farm in private. They will announce the decisions at the weekly meetings, rather than continuing to allow the other animals to have input. The animals are upset, and some begin to protest, but are intimidated into silence when
suddenly the dogs sitting round Napoleon let out deep, menacing growls.
Further, when Napoleon wants to starve the hens into submission, the dogs keep anyone from interfering with his cruelty.
A second method Napoleon uses to keep the animals from revolting is propaganda. Propaganda is telling lies or half-lies to forward a political agenda. With Squealer as his mouthpiece, Napoleon is able to twist facts. Squealer always has some explanation that makes what Napoleon is doing sound as if it is a great sacrifice for the benefit of the other animals. Napoleon is, in reality, a lazy, incompetent, narcissistic dictator, but Squealer paints him as a heroic leader. Napoleon also has his base in the sheep: they are so stupid he can use them to drown out dissent by cuing them to repeat the mindless slogans he has drilled into them over and over.
Napoleon's expert use of a violence and propaganda allows him to consolidate his power and intimidate his opponents. Orwell deploys him as a caution to people living in democracies: the wrong kind of leader can quickly become a tyrant.