How does the rebellion take place in Animal Farm?
The idea of rebellion is planted by Old Major, who is at the end of his life; he has a vision of a farm owned by Animals, who work together for the common good. His ideas are taken and expanded by the pigs, led by Snowball and Napoleon; Snowball is an idealist, while Napoleon seeks personal power. When Jones forgets to feed the animals, they rebel and drive all the humans off the farm, and believe themselves to be on the verge of a better future. The animals change the name of the farm from Manor Farm to Animal Farm, but this change is not accepted by the public until the Battle of the Cowshed, where the animals prove that they are capable of defending their property.
...human beings did not hate Animal Farm any less now that it was prospering... against their will, they had developed a certain respect for the efficiency with which the animals were managing their own affairs. One symptom of this was that they had begun to call Animal Farm by its proper name and ceased to pretend that it was called the Manor Farm.
(Orwell, Animal Farm, msxnet.org)
After that, although the humans make a few attempts to discourage the farm's success, the farm moves from its equality-based Utopian ideals to a slave plantation under the rule of Napoleon, and the rebellion is all-but forgotten, with only the memories -- many invented by Squealer -- of Napoleon's glorious victory over humanity to remember the rebellion by.
To answer this question take a look at Chapter Two. According to the narrator, the Rebellion "was achieved much earlier and more easily than anyone had expected." One Saturday evening, Mr. Jones goes out and gets so drunk that he forgets to feed the animals. Overcome by hunger, they break into the grain store and easily overcome Mr. Jones and his farmhands who, in response, flee the farm.
The animals are then left in complete control of the farm. They cannot believe their "good fortune" and how easy it was to expel all humans from the farm. Now the real work of the Rebellion can happen, beginning with the Seven Commandments, the framework through which the animals turn Old Major's vision (from his speech in Chapter One) into a reality. Specifically, the animals proclaim all humans to be enemies and all animals to be friends.
The expulsion of the humans and the creation of the Seven Commandments means that the Rebellion has taken place both physically and ideologically.
The novel Animal Farm, by George Orwell, depicts a rebellion by farm animals for their freedom from human tyranny. The rebellion is composed of three distinct stages: the secret meeting at the barn, the ostracization of farmer Jones, and the battle of the barn. Through each of these stages, the rebellion develops, and "officially" ends when Napolean says that the rebellion is over.
The meeting at the barn in the midst of night is the first step of the rebellion. The animals exchange thoughts and first congregate. Officially, the rebellion begins when Old Major initiates it by sowing the seeds of freedom with his speech about his dream and unifying them through the song, "The Beasts of England."
A rebellion is not a true rebellion without an action to overthrow an old idea or person. In the case of Animal Farm, the first "shot" is heard when the farm animals revolt because of farmer Jone's malnourishment and disinterest. The animals, bite, kick, peck, and otherwise tackle farmer Jones, and take the farm to themselves.
In the last stage of the rebellion, Jones attempts to exact his revenge and retake his farm. Jones brings guns and men, but fails to take the farm. After the animal's victory over Jones, the rebellion of Jones farm succeeds and the reknowned farm is hitherto known as "Animal Farm."