He'd first have to get used to the weight and balance. Naruto is used to his kunai and shuriken, which are much lighter. The lightsaber's energy blade would also be a new concept for him. He might start by simply holding it and getting a feel for it, like he did when he first learned to use a sword in the original series.
He could find it during one of his missions. Maybe he's exploring an ancient ruin and stumbles upon the lightsaber. It could be in a chest or just lying there, and Naruto, being curious, picks it up.
Naruto's fighting style would likely incorporate more acrobatic flips and spins to take advantage of the lightsaber's reach. He'd also use his shadow clone jutsu in new ways, like having clones surround an enemy while he attacks from above with the lightsaber.
In the fanfiction, the double lightsaber might be a gift from an unknown entity. Naruto, being the curious and adventurous type, would start training with it. He'd have to learn how to handle the two blades simultaneously, which could be a whole new challenge. This could lead to new forms of combat that blend Naruto's existing fighting styles with the lightsaber techniques.
For the female characters like Sakura, she might use her medical knowledge to understand the potential damage guns can do. She could then use her strength to wield a gun - sword hybrid weapon effectively. Ino might use her mind - control abilities in new ways. For example, she could make an enemy think they're being shot at by a gun when in reality it's just an illusion, while she attacks with her sword. And Hinata, with her gentle nature, would need some time to get used to the violent nature of guns, but would eventually find a way to combine it with her gentle - fist style and sword - handling skills.
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.
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.