One possibility is that Dumbledore discovers new evidence that clears Harry's name. Maybe there was a misused spell by the Ministry that made it seem like Harry was guilty. Dumbledore then uses his influence and magic to break Harry out of Azkaban and they begin to expose the real culprits behind the false accusations.
Obviously, Harry Potter himself is a key character as the story is about his release from Azkaban. Dumbledore is likely to be important too. He has the power and influence within the wizarding world to potentially free Harry. His wisdom and knowledge of the situation would play a big role.
Well, it could be that when Harry is released from Azkaban, he discovers new magical powers or abilities that he developed during his time there. He might then use these powers to fight against the dark forces that once put him in Azkaban. And he would surely have to deal with the psychological trauma of being in that awful place as he tries to move forward in his life.
One possible plot could be that Harry was wrongly imprisoned. Once released, he'd be on a quest to find out who framed him. He might start by gathering his old friends like Hermione and Ron. They would then dig into the dark secrets of the wizarding world that led to his false incarceration.
There could be some new characters introduced in the fanfic. Maybe a powerful wizard from a far - off land who has heard of Harry's plight and decides to help. Or perhaps a group of outcasts in the wizarding world who see Harry as a symbol of their own struggle against the unjust system and come to his aid.
Obviously, Harry himself is a key character. His own strength, both physical and mental, could play a role in his release. For instance, he might have developed some new magical abilities during his time in Azkaban that help him break free.
One possible scenario could be that new evidence is found to prove Harry's innocence. Maybe a powerful magical object reveals the truth about what really happened, leading to his release.
Maybe he uses some powerful magic spells that he has learned secretly. For example, the Patronus charm could be used to fend off the Dementors which are the main guards in Azkaban. He might also get some unexpected help from his friends or some mysterious characters within the fanfiction world.
It could be Sirius Black. Since he has his own experience with Azkaban, he might know some secrets about the place. He could return in some form within the fanfiction and assist Harry in his escape, maybe by leading him through some hidden tunnels or using some special skills he developed during his time in prison.