What techniques do Napoleon and Snowball use in their struggle for power over Animal Farm?
Snowball and Napoleon, arguably the most intelligent animals on the farm (other than, perhaps, the mule) are in a "battle" to control the direction that Animal Farm will take. Both of them choose different tactics during the fight, one which Napoleon will ultimately win.
Snowball seems to have a genuine interest in improving the lot of the animals on the farm. He is idealistic and believes in the "commandments." His main goals are to spread the revolution (as seen in his suggestion to send out more birds to visit other farms) and to improve conditions on Animal Farm. In a political sense, he is trying to win the hearts of the the animals and thereby their loyalty. He can do this if he is able to think of "programs" that appeal to the animals sense of progress (for example, the Windmill that is supposed to provide some creature comforts to the animals in the barn.) Technology is a way to improve the farm and allow the animals more time off. Sort of a populist message.
Napoleon, on the other hand, is more of a "blunt instrument." He is willing to spend the time needed to debate Snowball, but generally takes opinions contrary to Snowball in order to create conflict. His main goals are to tighten his control over Animal Farm and ensure its protection (as seen in his suggestion to acquire more guns rather than sending out birds.) He has had the foresight to train up a pack of attack dogs and make them loyal to him, showing that the "coup" option was always in the back of his mind.
Napoleon was willing to go through the "democratic" process to a point, but when it looked like he was going to lose the vote on the windmill he had his dogs chase Snowball off the farm, thus ending the debate. For him, politics is only a useful game if he was winning. He tends to work on the animals minds, twisting history and events in ways the less intelligent animals have problems recognizing. This twisting solidifies his power. Notice the way that once Snowball is gone, Napoleon decrees that the windmill will indeed be built because he had (supposedly) secretly always been for it.
In the end Snowball didn't stand a chance. He thought he was playing politics on a level playing field, but Napoleon was the type willing to just take the ball and go home.