One very good example is the use of statistics and numbers to "prove" that the Animal Farm is a success, despite the evidence of hunger and poverty in the animals themselves. For the pigs, this becomes an important strategy because they are easily able to confuse and convince the other animals; the more Squealer talks, the more confused the animals get, until they can't help believing him. While earlier in the novel Squealer simply thinks fast and makes up stories, reading the "facts and figures" to prove that they are all better off is much more credible, and since most of the animals can't read, they are unable to argue.
Reading out the figures in a shrill, rapid voice, he proved to them in detail that they had more oats, more hay, more turnips than they had had in Jones's day, that they worked shorter hours, that their drinking water was of better quality, that they lived longer... They knew that life nowadays was harsh and bare, that they were often hungry and often cold, and that they were usually working when they were not asleep. But doubtless it had been worse in the old days.
(Orwell, Animal Farm, msxnet.org)
Like the Soviet Union, the pigs use these fake reports and figures to keep the populace satisfied while using up most of the resources themselves. The reality is what the animals experience every day: they are hungry and cold, and work twice as hard to support the pigs. The appearence -- not tangible, but instead simply assumed -- is that they are better off only because Jones is gone; Jones represents the myth of the terrible past, and so things must be better now.
Orwell revisits the theme of appearance versus reality through Animal Farm. Most broadly, the animals' revolution is undertaken in order to achieve freedom and equality, and while it initially appears that they have accomplished this, there are many underlying inequalities and many ways in which they are less free than they imagine. The pigs claim an inordinate amount of resources (as in the apples and milk in Chapter Three) and justify their actions by pointing out that they are the "brains" of Animal Farm. This pattern continues throughout the book, culminating with the alteration of the Seven Commandments to read: ALL ANIMALS ARE EQUAL BUT SOME ANIMALS ARE MORE EQUAL THAN OTHERS.
Beyond this, Orwell uses Squealer to show how those in power can manipulate appearances to maintain and increase their control over society. Squealer is constantly framing Napoleon's clearly self-serving actions as being in the interest of all the animals. In addition, through his rhetoric, he creates a new reality in which Snowball, recast as a traitor, is constantly threatening the very existence of Animal Farm:
"Comrades!” cried Squealer, making little nervous skips, “a most terrible thing has been discovered. Snowball has sold himself to Frederick of Pinchfield Farm, who is even now plotting to attack us and take our farm away from us!...We had thought that Snowball’s rebellion was caused simply by his vanity and ambition. But we were wrong, comrades...Snowball was in league with Jones from the very start! He was Jones’s secret agent all the time."
Squealer goes on to reinvent Snowball's role in the Battle of the Cowshed, claiming first that he had acted in a cowardly way, and then even that he had fought on the side of the humans. The animals, while very confused, accept this, having become so confused about what is appearance and what is reality that they can no longer remember events that they have witnessed. It is not just that things are not what they seem on the farm. It is that the pigs are able to skillfully manipulate words in order to create a new reality, one which gives them more power over the rest of the animals.