They have known each other since elementary school when Tsukishima saved Yamaguchi from some boys who bullied him by calling them pathetic. Despite thinking that he was included among the ones Tsukishima insulted, Yamaguchi still grew attached to him and set his goal to become "as cool as him".
Yamaguchi calls Tsukishima by a nickname, "Tsukki", though the latter doesn't seem to mind. Although Yamaguchi is generally a shy person, he follows Tsukishima whenever he's mocking other people and snickers along. Yamaguchi also doesn't seem to mind whenever Tsukishima snaps at him, and he even apologizes for his behavior. He seems to care for and admire Tsukishima a lot. This is shown during the match against Aobajōsai; every time a serve was directed to Tsukishima and he didn't receive it properly, Yamaguchi was freaking out on the sidelines, but after Tsukishima finally received one, he was shown crying in admiration. He also often brags about Tsukishima to other people, though the aforementioned stays silent or tells Yamaguchi to shut up. They are barely seen apart from each other and are even in the same class in school.
At first, it seemed like Yamaguchi was simply following after Tsukishima without being thoroughly acknowledged by him, but Tsukishima truly cared for him and viewed him as a friend. When Yamaguchi succeeded with his jump float serve for the first time ever, Tsukishima complimented him and pointed out his hard work to the other teammates. However, with the time they spent at Karasuno, they grew apart in terms of effort they put into their training: while Tsukishima did only what he needed to, Yamaguchi trained even after team practices to work on his float serve. The situation escalated in the summer training camp as Tsukishima still refused to put in any more effort because he didn't see a reason to. Yamaguchi, who was frustrated by Tsukishima's way of thinking, yelled at him for the first time ever to have pride in what he does instead of giving up like this. This changed Tsukishima, who even called Yamaguchi "cool" for the first time ever, causing their relationship to recover.
Shimada is the one that taught Yamaguchi the jump float serve which became his forte. After watching Shimada play in the practice match against the Neighborhood Association, Yamaguchi went to his store and asked him to become his teacher. Since then, Yamaguchi often goes to Shimada Mart after closing hours to practice. Shimada acts like an older brother to Yamaguchi as well, often encouraging and cheering him on, and he also calls the younger boy by his first name. When Yamaguchi messed up during the Aobajōsai vs Karasuno match in the Interhigh, Shimada comforted him and motivated him to get back on his feet.
Though Yamaguchi usually assists Tsukishima in mocking Hinata, Yamaguchi and Hinata develop a friendly relationship as the year goes along. Yamaguchi is always there to try to keep Hinata from getting into too much trouble. When Yamaguchi was at a loss of what to do with Tsukishima during the summer camp arc, he asked Hinata for advice.
Though originally hated by Kageyama because he aided Tsukishima in picking on the setter, Yamaguchi and Kageyama eventually developed mutual respect for each other. Whenever Yamaguchi was switched into games and succeeded with his jump float serves, Kageyama would compliment him.
Yachi and Yamaguchi are good friends who get along well and can relate to each other. When Yachi first arrived with Shimizu to practice, Yamaguchi thinks of her as "cute." He's shy around her at first, but eventually they start to get closer. In the novels, Yachi comments that Yamaguchi is taller than she thought. Before their rematch against Aoba Jousai, Yachi offers helpful advice to Yamaguchi on how to handle his anxiety but ended up becoming anxious herself. When Yamaguchi succeeded with his jump float serve, Yachi seems to be brimming with pride. Yamaguchi seems to have a small crush on Yachi, as he's seen blushing around her at times.