Naruto might be really confused at first. He's used to people being friendly or having normal crushes, but a yandere is a whole different level. He'd probably try to talk to her and understand why she's acting so strangely.
In a fanfiction, Naruto could be training in a secluded area and Yandere Koneko stumbles upon him. She immediately falls for his spunk and the fact that he doesn't give up easily. Yandere Koneko then tries to insert herself into Naruto's life by bringing him food and small gifts. Naruto is initially confused but then realizes she has a rather extreme way of showing affection and has to gently set boundaries.
One idea could be that Naruto somehow gets trapped in a dimension where Kaguya has become a yandere for him. She tries to keep him there all to herself, while Naruto has to figure out a way to escape and also deal with her obsessive behavior.
Naruto might also feel a sense of responsibility. He might think that he did something to cause Yugito to act this way. So he could start to limit his own actions to avoid triggering her yandere behavior. For instance, he might stop being so friendly with other girls in front of her. But at the same time, he would not give up his own dreams and values, and would try to make Yugito understand that her behavior is not acceptable in a way that is both firm and kind.
At first, Naruto might be really confused. He's used to the normal Sakura, so when she starts acting all yandere, he'd be like 'What's going on, Sakura - chan?'. He'd probably try to talk to her and find out what's wrong.
Often, it starts with the yandere character becoming infatuated with Naruto. They might start by observing him from afar and then gradually insert themselves into his life. Their actions are driven by their extreme love which can border on possessiveness.
A more complex fanfiction could involve Yandere Chan being a part of an experiment by Orochimaru. He combines some of her yandere traits with ninja abilities. She then targets Naruto, believing he has some special power that she needs. Naruto has to not only deal with her attacks but also try to understand her motives and perhaps find a way to reverse Orochimaru's experiment on her.
One common theme is possessiveness. The yandere characters in these fanfictions often show extreme possessiveness over Naruto or other characters. For example, they might not allow the object of their affection to be around other people.
One common theme is overprotectiveness. The yandere little sister will go to extreme lengths to protect her loved one, often seeing others as threats. Another theme is possessiveness. She wants to have the sole attention of the person she's fixated on, like in many stories where she gets jealous of the protagonist's friends. Also, there can be themes of secrecy and hidden desires, where she hides her yandere tendencies until certain events trigger her extreme behavior.
One common theme is the extreme nature of the yandere's love. It's often possessive and can lead to some intense and sometimes dangerous situations for Naruto. Another theme is the struggle between Naruto's own values and the yandere's demands. For example, Naruto might value friendship and freedom, while the yandere wants him all to themselves.