In the book, Animal Farm, what are three ways Napoleon used fear to keep the animals under control?

First, Napoleon uses fear to maintain his power.  This might sound unimpressive, but words can bring great fear, and when fear is prominent, it possesses the power to control.  One of the refrains that Napoleon uses is: "You don't want Jones to come back, do you?"  To the animals Jones is the epitome of evil. Hence, the fear of Jones and their former way of life controls the animals to follow Napoleon.

Second, Napoleon uses...

First, Napoleon uses fear to maintain his power.  This might sound unimpressive, but words can bring great fear, and when fear is prominent, it possesses the power to control.  One of the refrains that Napoleon uses is: "You don't want Jones to come back, do you?"  To the animals Jones is the epitome of evil. Hence, the fear of Jones and their former way of life controls the animals to follow Napoleon.

Second, Napoleon uses the fear of Snowball to control the animals.  He persuades the animals that Snowball is a traitor.  He comes around in the darkness of night and sabotages things - like the windmill.  Hence, Napoleon has created a bogeyman to keep the animals obedient.  This forces the animals to work harder and create a new windmill.

Finally, Napoleon uses violence to make sure there is no rebellion.  In the beginning of the book, he trains the puppies of Jessie and Bluebell to become fierce attack dogs.  The other animals knows that if anyone of them gets out of line, they will suffer and died.  Hence, fear of physical harm controls the animals as well.