He might use the invisibility cloak. Harry could sneak into Azkaban unnoticed and then use magic to break Draco out of his cell. The cloak has served him well in the past, and it would be a simple yet effective way to get past the guards.
Harry could use his skills in apparition. He might have practiced and perfected the ability to apparate into Azkaban and then out again with Draco. However, this would be extremely dangerous as Azkaban's anti - apparition wards are very strong. But with his Gryffindor courage, he might take the risk. He could also use some spells to temporarily disable the wards before apparating. Another option is that he uses his connection with Dumbledore's old secrets. Maybe Dumbledore left behind some knowledge or items that can help him get through Azkaban's security. Harry could have found these in Dumbledore's old office or through some other means.
Harry might use polyjuice potion. He could transform into a guard or an official who has access to Draco's cell. Once inside, he could then use magic to free Draco and escape. This would require him to obtain some hair from the person he wants to transform into, which could be a challenge in itself. But if he manages to do it, it would be a clever way to bypass the security.
One possible plot could be that Harry discovers some new evidence that proves Draco's innocence. Maybe there was a frame - up by some dark forces within the wizarding world. Harry, being the hero he is, feels compelled to act and uses his influence and skills to break Draco out of Azkaban. This could lead to them having to go on the run together, hiding from the authorities while they try to expose the real culprits.
The plot could start with rumors reaching Harry that Draco is being unjustly treated in Azkaban. Harry, being the hero he is, decides to investigate. He uncovers a conspiracy within the Ministry of Magic that is trying to keep Draco locked up for political reasons. Harry then uses his connections, like his friendship with Neville who now has some influence in the Ministry, to get a hearing for Draco. During the hearing, Harry presents the evidence he has found, which includes magical artifacts that prove Draco's innocence, and Draco is finally released.
Harry might survive in Azkaban because of his connection to his friends, even if they betrayed him. Their memories could give him the strength to hold on. And he may be able to use his magic in unique ways. He could draw on the positive emotions he has left, like his love for his parents, to create a shield against the Dementors. Plus, he may be constantly looking for a way to prove his innocence and that hope could keep him alive.
One possible fanfiction could involve Harry finding out that Draco was wrongly imprisoned in Azkaban. Harry might use his influence and his skills as an Auror to dig deeper into Draco's case. He could discover evidence that clears Draco's name, like finding out that Draco was framed by some dark wizards who wanted to get rid of the Malfoy family's influence. Then, Harry would have to fight against the bureaucratic system of the Ministry of Magic to get Draco released.
In some fanfictions, Harry might use powerful magic he's learned secretly. For example, he could discover a new spell that can break the Azkaban's defenses. He then sneaks into Azkaban, locates Sirius, and uses this spell to free him from his cell. Maybe he also has to fight off some Dementors on the way out.
Well, in some fanfictions, Harry might use some hidden magic he discovers in Azkaban. Maybe he finds a way to turn the Dementors' power against Voldemort. Since Dementors can suck out a person's soul, Harry could somehow direct them towards Voldemort, weakening him enough to deliver the final blow.
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.
In this kind of fanfiction, it could happen in various ways. Maybe Hermione discovers some evidence that Draco was wrongly accused. For example, she might find that certain spells were cast on Draco to make him seem guilty when he actually wasn't. So she uses her intelligence and knowledge of magic to expose the truth and save him from Azkaban.
In some fanfics, he might use powerful magic that he has secretly mastered. Maybe a new spell that can create a portal right out of his cell.
It could be Hermione. She's always been smart and resourceful, and she might have found evidence to prove Harry's innocence and get him released.