Student was the term used to describe an individual or group who were taught by a teacher, usually in a classroom. (DS9: "The Nagus"; VOY: "Gravity") Younger students were sometime recognized as a pupil or a school kid, while a fellow student was known as a classmate.
In 2151, Hoshi Sato taught a linguistics class of twenty-one students at a university in the country of Brazil on Earth. One of her students had trouble pronouncing words of an alien language. (ENT: "Broken Bow")
The same year, the students of Miss Malvin's class from Worley Elementary School in Kenmare, County Kerry, Ireland on Earth sent letters and drawings along with questions to the crew of Enterprise NX-01. (ENT: "Breaking the Ice")
In 2369, Miles O'Brien took over teaching duties at the school on Deep Space 9 from his wife, Keiko O'Brien, while she was off-station on Earth. In her stead, Chief O'Brien assigned the older students to write an essay on ethics, when Nog failed to turn in the essay he claimed that Vulcans had stolen his homework, as they had no ethics. (DS9: "The Nagus")
In 2369, a group of Orthodox Bajorans, lead by Vedek Winn Adami, objected to Keiko O'Brien's scientific teaching methodology to her school students. O'Brien taught the children about the Bajoran wormhole without mentioning the Bajoran religious beliefs relating to the phenomena. (DS9: "In the Hands of the Prophets")
Doctor Julian Bashir also spoke of himself as a "star pupil". When he told Miles O'Brien about his past, he mentioned that when he returned to Earth after he was genetically enhanced he and his parents had to move to a different city and he was enrolled in a new school using falsified records. Instead of being the slowest learner, he was the star pupil. (DS9: "Doctor Bashir, I Presume")
Chakotay compared Seven of Nine and Kathryn Janeway to a pupil and a mentor. (VOY: "Hope and Fear") Seven of Nine was also seen as a pupil by The Doctor and the Borg Queen. (VOY: "Latent Image", "Dark Frontier", "Someone to Watch Over Me")