He'd use his ninja training. Naruto has always been good at adapting in his own world, so he'd likely rely on his skills and instincts.
In this fanfiction scenario, Naruto could bring his ninja skills to the Def universe. He'd probably have to adapt to the new environment. For example, if the Def universe has different laws of physics, his usual jutsu might not work the same way. He might also learn new techniques from the Def universe and combine them with his own.
Naruto would adapt in several ways. Firstly, he'd use his ninja skills in new ways. For example, his speed and agility could be useful in modern jobs like delivery or security. Socially, he'd be curious about modern relationships and would quickly learn the norms. He'd also adapt to modern education systems if he decided to study, using his eagerness to learn. And he'd be fascinated by modern forms of entertainment like movies and video games.
Naruto would adapt by using his ninja skills. His speed and agility from being a ninja would help him in exploring Earthland. He could also use his rasengan as a powerful attack against any potential enemies. He might start by finding a place to stay and learning about the local customs.
He'd probably start by observing. Naruto is curious, so he'd watch how the Asgardians live, their customs, and how they interact. Then he'd start to adapt by using his ninja adaptability skills.
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.
He would need to understand the social hierarchy in Kirigakure. In Konoha, he was used to a certain way of doing things, but in Kirigakure, there could be different rules regarding how ninjas interact with each other and with the village leaders. For example, he might have to show more deference to the Mizukage than he did to the Hokage. Also, he'd have to adapt to the food. Kirigakure is near the sea, so there would be a lot more seafood in his diet.
Sasuke would likely be very cautious at first. He'd be observing everything closely, trying to figure out the rules of this strange place. His Sharingan might give him an advantage in seeing through some of the illusions in Wonderland. Naruto, on the other hand, would probably be more excited and jump right into things, ready to make friends with the odd - looking creatures.
To adapt to being the Mandarin, Naruto would first need to understand the nature of the ten rings. He might start by experimenting with each ring's individual power. He'd then figure out how to combine these powers with his existing ninja abilities like rasengan. His relationships with other characters would also change. Some might be afraid of his new power, while others would see it as an opportunity to fight against greater threats. Naruto would have to convince them that he can be trusted with this power and that he'll use it for the greater good.
He would likely start by observing. Just like how he was trained in the ANBU to be aware of his surroundings. He'd watch how the classes are conducted, how the students interact with each other and the teachers. Then he'd start to adapt by using his ninja skills in a way that fits the Hogwarts environment. For example, using his speed to get around the castle quickly.
Naruto would adapt slowly. At first, he'd be confused by the different lifestyle. But his adaptable nature would help. He might start by learning about the local customs and trying to fit in at school. He'd use his ninja skills in secret, like using his speed to be on time for classes when he oversleeps.