In the opening of Chapter 2, Snowball is described as the best known of the male pigs (aside from Napoleon and Snowball). He could "turn black into white" because he was a very persuasive talker.
He was a brilliant talker, and when he was arguing some difficult point he had a way of skipping from side to side and whisking his tail which was somehow very persuasive.
Notice that as Squealer is being hailed for his persuasive speech, it is his "skipping from side to side and whisking his tail" that made him persuasive. This indicates that he was good at distracting those he spoke to and he was very good at changing his positions (going from side to side) in order to win arguments or in order to justify his new positions.
There are many times in the novel when the commandments are changed and Squealer is able to fool the animals that the commandments have not been changed. Therefore, he is able to change his position (from black to white) without the animals even knowing it. At the end of Chapter 6, the pigs start sleeping in beds. This contradicts the initial fourth commandment which stated that "No animal shall sleep in a bed." When Clover suspects something, Muriel spells out the commandment which had been updated to state that "No animal shall sleep in a bed with sheets." Squealer assures them that the commandment was always stated in this way: to only outlaw beds with sheets.
You did not suppose, surely, that there was ever a ruling against beds? A bed merely means a place to sleep in. A pile of straw in a stall is a bed, properly regarded. The rule was against sheets, which are a human invention.