One interesting plot point could be how Harry devises the plan to break Sirius out. Maybe he uses his invisibility cloak and some clever spells. Another could be the reactions of the other characters when they find out, like Hermione's concerns about the legality and consequences.
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.
Well, perhaps he uses some powerful magic he's learned secretly. Maybe he has help from unexpected allies, like a magical creature that can bypass the prison's defenses.
It varies in different fanfictions. Some have Harry at 12, while others might depict him as 14 when this event occurs. It depends on the author's imagination and the story's plot.
Perhaps Voldemort has some inside help. He could have bribed or threatened one of the guards or even a Ministry official who has access to Azkaban. This person could then help him get in and break Harry out. Or he might have found a secret passage into Azkaban that the Ministry doesn't even know about, and he uses that to his advantage.
One reason could be that Voldemort wants to use Harry for his own gain. Maybe he thinks he can turn Harry to the dark side and use his power for some grand evil plan. He might believe that with Harry on his side, he can finally defeat all his enemies and rule the wizarding world completely.
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.