How did Sirius escape from Azkaban?

Question

It always amazed me to think that Sirius Black somehow (allegedly) became the first person (at the time of the third book) to escape from Azkaban.
Now, I can't really remember exactly what happens in the books (read it years ago) but I have a vague feeling that it was not particularly explained.

• Did he get help?
• Did he pull a Shawshank Redemption?
• Am I just forgetting a major plot point, like OOTP breaking him out somehow without the ministry knowing about it?

Is there any canon explanation of exactly how Sirius managed to escape from Azkaban Prison? Which is a high security, magical, dementor infested prison; not to mention a prison filled with Death Eaters who probably despise him and would definitely try to stop his escape.

Answer 1

Sirius explains in the third or fourth book that the thought of his innocence and revenge kept him from being affected by the Dementors. He later says that he got a Daily Prophet and saw Peterpettigrew after that he knew he had to escape so he did. Quoted from the Harry Potter answer wikia:

His knowledge of his innocence allowed him to retain his powers and sanity. 'One night, when (the Dementors) opened my door to bring food, I slipped past them as a dog. It's so much harder for them to sense animal emotions that they were confused ... I was thin enough to slip through the bars. I swam as a dog back to the mainland. I journeyed north and slipped into the Hogwarts grounds as a dog. I've been living in the Forest ever since.' Prisoner of Azkaban; chapter 'The Servant of Lord Voldemort'http://harrypotter.answers.wikia.com/wiki/How_did_Sirius_Black_escape_from_Azkaban

This Quote is from the Harry Potter wikia, but its sort of conjectural(at least the article said that), it matches the other answers though

In 1993, Sirius Black escaped from Azkaban after seeing Scabbers in a Daily Prophet article, of the paper Cornelius Fudge gave him, in July 1993, recognising him as his traitorous former friend Peter Pettigrew. By 1 August, Black took advantage of his extreme weight loss to slip through his cell door in his Animagus dog form (which was unregistered, thus the Ministry did not take preparations against) while the Dementors were bringing in his food and swam across the North Sea to find Pettigrew.[2]Black was able to maintain his sanity due to his knowledge of his innocence, a non-happy thought that the Dementors could not take. It was only this that allowed him to maintain his powers to transform, and what made the escape possible.

This escape was the only known unaided escape, and officially the first one in Azkaban history (until Barty Crouch Jr.'s escape was revealed). Black was facing the Dementor's Kiss as punishment should he ever be recaptured, though he ultimately eluded the Ministry, and his name was cleared shortly after his death at the hands of Bellatrix Lestrange in the Department of Mysteries.http://harrypotter.wikia.com/wiki/Azkaban_escapes

And this link is to a question from the movies stack exchange- https://movies.stackexchange.com/questions/11314/how-did-the-death-eaters-physically-escape-from-azkaban

It explains the mechanics to escape.

Answer 2

Sirius explains the mechanics of his escape himself in Prisoner of Azkaban (emphasis mine):

“It was as if someone had lit a fire in my head, and the dementors couldn’t destroy it. … It wasn’t a happy feeling … it was an obsession … but it gave me strength, it cleared my mind. So, one night when they opened my door to bring food, I slipped past them as a dog. … It’s so much harder for them to sense animal emotions that they were confused. … I was thin, very thin … thin enough to slip through the bars. … I swam as a dog back to the mainland. … I journeyed north and slipped into the Hogwarts grounds as a dog. I’ve been living in the forest ever since, except when I came to watch the Quidditch, of course. You fly as well as your father did, Harry. …”