They could start by trying to understand the different rules of that world. Since Batman's world is more grounded in detective work and street - level crime fighting compared to the Avengers' world of superpowers and global threats. The Avengers might use their powers to help solve some of the complex mysteries in the Batman fanfic world. For example, Vision could use his ability to see through objects to find clues that Batman might miss.
The Avengers could interact with the characters in the Batman fanfic in various ways. Maybe they would form teams to take on the villains. Iron Man and Batman could collaborate on creating new technology to fight crime. The more morally upright Avengers like Captain America could have some interesting discussions with Batman about justice and the limits of power. And the Avengers' powers could be a huge advantage in some of the larger - scale threats that the Batman fanfic world might face, like if a super - villain from another dimension invaded.
He might fit in as a sort of mentor figure. He has years of experience fighting crime in Gotham. He could teach the younger Avengers like Spider - Man (if he's in the mix) some valuable lessons about perseverance and the importance of a strong moral code. Also, his physical combat skills would be useful in hand - to - hand battles against powerful foes.
The Joker from Batman Begins could play a really interesting role. He might see the Avengers as a new kind of chaos to introduce. He could try to manipulate some of the more hot - headed Avengers like Thor. He would play mind games with them, which would be very different from the usual physical battles they face. Batman would then have to step in and use his understanding of the Joker to stop him from causing too much division within the Avengers.
Batman joining the Avengers in a fanfic could be due to a common enemy like a super - intelligent villain who has been causing chaos in both the DC (Batman's world) and Marvel (Avengers' world). Batman might initially be a bit of an outsider among the Avengers. But his no - nonsense attitude and ability to plan ahead could earn their respect quickly.
Tony could use his technology to analyze the popularity trends in Yelena fanfiction. He might say 'I can see which scenarios are the most popular in these fanfics about Yelena.' Natasha might take some of the positive portrayals in the fanfiction as a compliment to her sister. She could say 'This shows that Yelena is making an impact.' Thor might not fully understand but he could share the fanfiction stories in Asgard as a strange but interesting Midgardian thing.
They could interact through Batman's dreams. Athena could visit him in his sleep, sharing her wisdom and giving him cryptic messages that he then has to decipher in his waking life to solve crimes or deal with threats in Gotham.
He would be a bit of an outsider at first. The Avengers are used to a certain dynamic, and Batman's lone - wolf style would be different. But he could offer his strategic mind. Maybe he'd start by analyzing each member's strengths and weaknesses, like he does with his foes in Gotham.
One possible plot could be that Batman's Gotham is threatened by a powerful villain who has some connection to the Avengers' universe. Maybe Loki decides to cause chaos in Gotham as part of a larger plan against Earth. Batman, being the detective he is, starts to investigate and soon realizes that this is no ordinary criminal. He then somehow gets in touch with the Avengers, perhaps through SHIELD's intelligence network. Together, they combine their skills and resources to take on Loki and his minions. Batman's stealth and strategic mind would complement the Avengers' superpowers.
They would interact in different ways. Captain America would be very friendly and helpful, like he is. He might volunteer at community centers. Iron Man would be a bit more aloof but still interact when it comes to business or innovation. Thor might not understand some of the modern human ways at first, but he'd be friendly in his own way. Hulk would probably stay away most of the time to avoid scaring people.
A human could interact with Pokémon through training. By teaching them new moves and strategies, they build a connection. For example, in battles, a trainer gives commands which the Pokémon follows.
They might start off a bit warily. The Howling Commandos could be skeptical of the Avengers' powers at first. But then they would realize that they can all contribute to a common goal. For instance, Thor's lightning could be used in a way that the Commandos had never seen before, and they could offer their knowledge of stealth and guerrilla warfare to the Avengers.