Miyuki Shirogane is the boy that Kaguya likes, but is unwilling to openly admit it to him, knowing that whoever confesses their love is the loser in a relationship. Her instincts and her pride as the daughter of a Shinomiya prevents her from doing so. Leading her to start mind games to corner Miyuki and make him confess which the latter is also doing.
In contrast to Miyuki, Kaguya believes a relationship should have both sides knowing everything about the other, leading her "Ice" personality (which initially met Miyuki) to resurface after the Culture Festival, believing that he should love that part of her as well if they should be in a relationship. Upon learning that Miyuki hides the "weak" parts of himself and believes he needs to be "perfect" in order to have anything in life, including a relationship with her, she shows increased concern and confronts him about it outright.
While they meet in spring of their freshman year, Kaguya actually doesn't notice him until he challenges her with exams. Miyuki's victory not only results in Kaguya recognizing him as an individual, but impresses the entire school.
Kaguya is presumed to fall for him sometime in his first year as the student council president, where he dives into a swamp (the same swamp Kaguya dived in to save someone from drowning) to rescue the ribbon she wears in her hair.
After chapter 160, they officialy started dating.
Ai Hayasaka is Kaguya's personal valet. Her mother is Kaguya's mother's wet nurse and they have been together since they were 7 years old, upon the formalization of their master-servant relationship. Only Kaguya fully understands Hayasaka's flaws and only Hayasaka fully understands Kaguya's. It was stated that their bond was similar to that of "inseparable sisters". Initially, Hayasaka hides her annoyance with some of Kaguya's treatment of her and her assigned workload, however after being encouraged by Miyuki, she confides her feelings in a rap. She also expressed her desire to have male friends. In response, Kaguya arranges to lighten Hayasaka's workload at home. Despite being weary of her friendship with Miyuki, Hayasaka assures her that she harbors no romantic feelings for him.
After Kaguya and Miyuki start dating, Kaguya's mindset turns increasingly cocky/all-knowing about relationships, much to the irritation of Hayasaka, who has never had a boyfriend before. Kaguya's gushing about her relationship reminds Hayasaka of her lack of a love life so much that she now actively runs away from Kaguya whenever the topic arises. Kaguya is still shown to be blissfully unaware of this and only seeks to talk to someone about how happy she is with her relationship.
Chika Fujiwara has been friends with Kaguya since middle school. At times Kaguya detests her and her friendly nature oftentimes because Fujiwara mostly gets things that Kaguya cannot get (e.g. Miyuki's lunchboxes, Kei and Fujiwara's BFF-ness, getting married to Miyuki at a board game, etc) calling her the incarnation of avarice and greed, vile woman, personification of sexual desire. Despite Kaguya thinking about Fujiwara like that at times, she finds her friendship with her irreplaceable in its own way, enough for her to say that it has the same weight as her like for Miyuki.
Yu Ishigami is Kaguya's underclassman. At times she shows concern for him as his senior and at times she just wants to kill him due to him accidentally interfering in her plans. While normal students scorn Ishigami she has openly said that Ishigami is someone worthy of her attention based on what she has personally seen. She has helped him study to not be held back a grade and supports his crush on Tsubame Koyasu. Being aware of the truth regarding Ishigami's suspension in middle school, Kaguya reveals Kou Ogino's actions to VIPs at Shuuchin Academy and forces him to transfer. When Kyoko Ootomo visited the school to see Ogino and insult Ishigami, Kaguya wanted to hurt her but is refrained from doing out of respect for Ishigami's efforts to protect Ootomo's smile. Kaguya's upperclassman-underclassman relationship with Ishigami develops as time goes on and is shown to occasionally prefer him over Chika (much to Chika's dismay).
Kei Shirogane is a girl Kaguya wants to get on good terms with. Her longtime desire for a little sister gave birth to her desire to have Kei to call her "Sis", and Kaguya is very much willing to go to great lengths for it to happen.
Miko Iino is a friend of Kaguya. Kaguya considers her as a "Good girl", saying that a few times when Miko points out her and Shirogane's antics looked like flirting. She also called her a "Good girl" at a time when Miko eased Kaguya's insecurity by having the lowest amount of bellmarks gathered by the whole student council.
Nagisa Kashiwagi is a friend of Kaguya. They frequently ask advice from one another regarding their own romances (albeit Kaguya still hides under the guise of asking for a friend). After watching Kaguya interact with Miyuki in the Student Council room, Nagisa realized that Kaguya likes him and that her "friend" is actually Kaguya herself. During the Cultural Festival, she discreetly helps Kaguya spend time with Miyuki.
Maki Shijo is Kaguya's second cousin twice removed. As a part of a distant branch of the Shinomiya family, she openly dislikes Kaguya and calls her Auntie/Old lady as Kaguya is two generations above her, though the two start getting along after the events of Chapter 168.
Gan'an Shinomiya is Kaguya's father. The two are implied to have a very distant relationship, as Kaguya mentions that he has never shown her any form of parental affection.