Harry would rely on his basic values. His loyalty and courage would still be his strong suits. He might join a group of young wizards who are working on some noble cause in the future magic world. Through interacting with them, he'd gradually understand the new rules and customs. For example, if there are new dueling regulations, he'd learn them in the process of joining friendly duels.
He'd first have to get used to the new technology. If there are new magical devices, he'd need to learn how to use them. For instance, if there are advanced wands with extra functions, it would take him some time to figure them out.
In a 'Naruto travel to the future fanfiction', Naruto would adapt through his strong sense of curiosity. He would be eager to explore every new thing he sees in the future. His resilience would also play a big role. If he encounters difficulties, like not understanding how a particular future - tech works, he won't give up. Instead, he'll keep trying until he figures it out. And his ninja training gives him discipline. He would use this discipline to study the new ways of life in the future, from the social norms to the technological advancements.
The marauders would probably have to adapt their way of thinking. In the future, the concepts of right and wrong, good and bad might have shifted. They'd need to understand these new perspectives to fit in.
They'd probably start by observing how things work. The Titans are smart, so they'd quickly pick up on new technology and social norms. For example, if transportation is different, they'd figure out how to use it.
It could work through a time - turner like device. Maybe an ancient and more powerful version of the one Hermione used. This device might have been created by a powerful wizard in the past and Harry stumbles upon it in Hogwarts. It allows him to set the time and date he wants to travel to, which in this case is 1970.
Hermione would start by studying all the new things she could find. Ron would follow Harry's lead most of the time. Harry would use his instincts to figure out who to trust in this new future.
Well, he might find a world where magic has been completely integrated with Muggle technology. For example, broomsticks are now used for inter - planetary travel and there are magical apps on smartphones. Also, Hogwarts could be a much larger and more diverse place, with students from all over the universe coming to study.
He might be shocked. In fanfiction, the future could be full of strange twists. For example, if his friends' children are involved in some wild adventures that are very different from what he expects. He would probably be confused at first, then curious to understand how things got to that point.
Harry would need to learn about the different magical laws in America. For instance, the regulations regarding magical creatures might be stricter or more lenient compared to the UK. He might also have to get used to the different currency used in the American wizarding economy.
He'd probably use his magical training to his advantage. His physical fitness from all the running around Hogwarts and fighting dark forces would help him on the pitch. Also, his ability to stay calm under pressure, like when facing Voldemort, would be useful during important soccer matches.