The first example is found soon after the Rebellion with the disappearance of the milk and the windfall apples. When the cows have not been milked for some time and their udders are filled to bursting point, the pigs take to milking them, resulting in five frothy, pails of milk. The animals all wondered what was to happen to the milk. When they returned from work, they found that the milk had disappeared. On a query, it was discovered that the milk was to be mixed in the pigs' mash. If all animals were to be treated equally the milk should have been shared equally amongst all the animals.
When windfall apples were discovered, these were also claimed by the pigs. All the apples thereafter would then be reserved solely for the pigs. Once again, the idea of all animals being equal was ignored in favour of the pigs.
Another example is when the pigs moved into the farmhouse. The other animals had to make do with sleeping in the barn. The pigs were comfortably ensconced in the Jones' beds. It was clear that the pigs afforded themselves certain privileges, which were denied the other animals. For there to have been equality, all the animals should have been afforded exactly the same privileges that the pigs had.
A third example is the fact that the pigs never performed any physical labour. The arduous physical tasks were performed by all the other animals, under the supervision of the pigs. The pigs gave instructions and commandeered the rest of the animals, without lifting a single trotter to actually work.
Obviously, to avoid any dissent from the other animals, Squealer was sent by Napoleon to firstly, change the commandments so that the animals would be confused, since they could not clearly remember the original commandments due to poor intellect, and, secondly, Squealer made it his duty to explain to the animals why the pigs were so favoured. In the case of the milk and apples he mentioned that these were 'brain food' for the pigs. Since they had to run the farm and plan everything, they had to keep up their intellectual capacity. For them to fail in this most complicated task would mean that Jones would come back. Obviously none of the animals wanted that and accepted Squealer's explanation.
When the pigs slept in beds, the commandment was changed from: 'No animal shall sleep in a bed' to, No animal shall sleep in a bed with sheets. This appeased the animals since they could not remember the original version. Furthermore, it became custom to accept that the pigs would supervise and lead, since it was a known fact that they were the most intelligent animals on the farm and no one complained about them not performing any physical labour.
And so it came to be that the pigs exploited the other animals so that they could enjoy lives of privilege and luxury, just as Jones did. The other animals were no better off than they were during Jones' reign.