The apprentice could learn unique jutsu from Orochimaru. Since Orochimaru is known for his forbidden jutsu, the apprentice might gain an edge in combat but also face the danger of being corrupted by the power. They could then use these skills in battles against common enemies. And, in the process, they might try to redeem Orochimaru in some way, like showing him that there is a better path than his thirst for power.
One possible plot development could be Naruto struggling with Orochimaru's dark teachings while still holding onto his own sense of justice. Maybe he tries to find a way to use Orochimaru's knowledge for good. For example, he could learn some unique jutsu from Orochimaru and then modify them to be less harmful or more in line with Konoha's values.
The storyline could be very dark. Naruto, as Orochimaru's apprentice, might be forced to learn some forbidden jutsu. He would probably be in a constant moral struggle. Orochimaru is known for his unethical experiments, and Naruto could be made to assist in them. However, Naruto's inherent goodness might lead him to try and subvert Orochimaru's plans from the inside. Maybe he would pretend to go along with Orochimaru's ideas while secretly finding ways to undermine his power and free the other captives in Orochimaru's lair.
Well, Naruto could potentially be used as a bargaining chip by Orochimaru. Orochimaru might try to trade Naruto for something he wants from Konoha, like secret jutsu scrolls or some kind of political power within the village. And Naruto, being the determined hero he is, would likely be constantly looking for a way to escape and foil Orochimaru's plans.
In some fanfictions, Naruto might go to Orochimaru seeking power. He could be tempted by Orochimaru's knowledge of jutsu. Maybe he thinks that by learning from Orochimaru, he can become stronger faster and be better able to protect his friends and the village.
Naruto could learn the art of poison from Sasori. Since Sasori was known for his use of poison in his puppets, Naruto might find a way to use it defensively, like coating his kunai with a non - lethal poison that just immobilizes enemies.
He might learn Orochimaru's signature snake - related jutsu, like the Hidden Shadow Snake Hands. This jutsu allows the user to summon snakes from their sleeves or other hiding places to attack opponents.
One possible scenario is that Naruto would gain a lot more knowledge about the village's history and politics. The Sandaime, being an experienced Hokage, could teach Naruto about the different clans in the village, their relationships, and how to manage them. Naruto might also learn more advanced jutsu more quickly, as the Sandaime could give him personal training. This could make Naruto a much stronger ninja at a younger age and perhaps change the course of some of the earlier story arcs.
Well, Naruto might use his Nine - Tails chakra to break free. He's a tough one. He could also try to outwit Orochimaru with his ninja skills. Maybe he'd pretend to be unconscious and then surprise Orochimaru when he least expects it.
In the fanfiction, Naruto being taken by Orochimaru could lead to a whole new set of character developments. For one, Naruto's view of the ninja world might change. He's used to the relatively 'good - guy' environment of Konoha. But with Orochimaru, he'd be exposed to the more underhanded and cruel aspects of the ninja world. His relationships with his friends could also be put to the test. His friends would surely try to rescue him, and Naruto would have to decide whether to rely on them or try to handle things on his own while in Orochimaru's clutches.
In a fanfiction where Naruto and Hinata join Orochimaru, one possibility is that they are forced into it. Maybe Orochimaru has some kind of leverage over Konoha that makes them comply. Naruto, being the head - strong character he is, would likely be constantly looking for a way to escape and take Hinata with him. Hinata, on the other hand, would probably be more reserved and observant, trying to find Orochimaru's weaknesses.