The pigs of Animal Farm became the leaders because they were able to convince the rest of their comrades that they were the most intelligent and best suited to do so. They were at least partially right: The other animals bought into the pigs' story, and because most of them could not see that the pigs were primarily using the others for their own self-interests, they fell into the trap that the pigs were better suited to give orders rather than do their fair share of the farmwork.
As for the three leaders, Napoleon was a "rather fierce-looking Berkshire boar," the only one of his type on the farm. Because of this, Napoleon believed that he was better than the other pigs. He was far less inventive than Snowball, who was "vivacious" and "quicker in speech." Snowball proved to be a great organizer and teacher, and he was the most courageous of the swine, leading the attacks at the Battle of the Cowshed. Squealer was a "brilliant talker," a small, fat pig with "twinkling eyes." Deception proved to be his trademark, and he became Napoleon's right-hand "man."