He might rely on the kindness of others. In the Naruto world, there are many kind - hearted people. For example, he could get some food from the villagers who start to see his true self. Maybe Iruka sensei would share his food with Naruto from time to time.
Naruto could also try to hunt or forage in the wild. Since he has ninja skills, he can track small animals and catch them for food. And he can identify which wild plants are edible. It's a tough way but it's a possible survival method for him in this situation.
In such a fanfiction, Naruto might start by relying on the kindness of his friends. For example, Sakura could offer him some food from time to time. He could also look for odd jobs around the village, like helping with construction or farming, even if it's not something he's used to. Another possibility is that he might barter his ninja skills for food. Maybe he'll offer to protect a local merchant's goods during transport in exchange for a meal.
He might rely on his chakra. In the Naruto universe, chakra is a form of energy. Some fanfictions might suggest that Naruto could use his chakra to suppress his hunger for a while, although this is not a long - term solution.
He survives through his strong will. Naruto has an unwavering determination that refuses to be broken by Orochimaru's experiments. His inner strength and the chakra of the Nine - Tails within him might also play a role in withstanding the physical and mental torture of the experiments.
One reason could be that he is being ostracized by the village and no one is willing to hire him for regular jobs. So he has no income source to buy food.
One reason could be that he's not getting paid enough for his ninja missions. Maybe the village is facing financial difficulties and has to cut back on mission rewards. Another possibility is that Naruto is too generous and gives away most of his money to those in need, leaving him with little for himself. Also, he might have some unexpected debts that he has to pay off, which leaves him short on funds for food.
He might rely on his physical strength and martial arts skills. Just like Rock Lee in the original series who doesn't have much chakra but is a great fighter through intense physical training.
He uses his ninja skills, of course. His shadow clone jutsu can be very useful for scouting and distraction. And his Rasengan is a powerful attack that can fend off many threats.
He might survive through his own sheer willpower. Naruto has always been a tenacious character. So, even when left for dead, his determination to live and achieve his dreams could keep him alive against all odds.
Another character could come to his rescue. For instance, Sasuke might show up at the crucial moment. Despite their complex relationship, Sasuke still values Naruto as a friend or rival. He intervenes and stops Sakura from killing Naruto. Or perhaps Kakashi, Naruto's teacher, arrives in time. He uses his Sharingan or some other jutsu to neutralize Sakura's attack and save Naruto.
He could rely on his wits. Naruto is a clever kid. He might figure out how to forage for food, like finding edible plants or fishing in nearby streams. Also, he could use natural shelters like caves to stay safe at night.