Squealer had an innate understanding that people can be quite naive when it comes to their political establishments. At a fundamental level, Squealer understood that people wish to believe that their government is authentic and possesses a sense of legitimacy to it. Squealer appeals to this psychological basis in his drive to stipulate to the government's credibility in both the present and in recreating the past. Through this, Squealer understands that at its most basic and foundational psychological basis, the body politic does not want to believe that their government is not valid. Such a premise allows people to embrace what might be false to be true. It's not as if they willingly believe in falsehood, but rather allow themselves to be persuaded by Squealer's talent of "spin" and presentation of image. It is this "naive craving for symmetry and unity" as where Squealer begins his attempts and from this point he is able to find a great level of success in appealing to people based on their own psychological basis.
Squealer did a good job using the persuasive appeal of logic to prove to the animals that what they thought was true was indeed false. Squealer very carefully used his own voice to convince them as well. For example, the animals were sure they were not eating as much now as they had when they were with Mr. Jones. Their stomachs told them so. The crafty Squealer would check his record-keeping books and sure enough be able to prove by the percentages and the statistics that they were indeed harvesting much more food.
He also staged scenario to help the animals minds think something is true. The footprints around the windmill leading to the other farm made Squealer and Naploeon concoct another story about Snowball.
Since the animals could never prove the pigs wrong with evidence, Squealer got away with this.