in the book "Animal Farm" how does Napoleon obtain/ maintain power?

Napoleon uses fear and manipulation to obtain power over the other animals. He uses Squealer as his mouthpiece, to put a positive spin on his edicts/actions so that the animals follow him rather than Snowball. He allows the animals to believe that pigs are smarter than others and must be treated with more respect. He keeps the animals working hard so that they haven't the time to think for themselves or develop their intellects. He appropriates the puppies and trains them to be attack dogs who answer only to his call.

Hope this helps.

Animal Farm Napoleon Power

Napoleon rises to power by tricking all the animals to follow him. The animals aren t smart enough to realize what Napoleon is doing. One way Napoleon does this is by telling the animals Jones will come back. He also uses Squealer to to put a positive spin on his actions.

We see the first of many examples when Napoleon takes nine puppies from their parents and begins raising them himself. No one knows exactly what he is doing until the dogs suddenly appear, fully grown, to chase Snowball off the farm.

After Snowball is exiled, Napoleon is in complete control of the farm. He speaks relatively little because he has Squealer do his speaking for him.

From Shmoop

I think he eats the chickens, pisses on their plans, and kills the old plodder horse once he can no longer work. But you better check since I read that book 40 years age. There is much more like that, that the pig does as well.