A school is an institution in which teachers foster student learning.
The USS Enterprise-D, as a ship carrying families, included a school with various classrooms. The ship's children attended this school where they learned subjects such as literature, math, art, and botany. Several teachers worked in Enterprise's school, including Miss Kyle. At least one of the classrooms on the Enterprise contained a two-way mirror, allowing individuals to observe the classroom activities unseen. (TNG: "When The Bough Breaks", "New Ground", "Hero Worship", "Imaginary Friend")
During an attempt to take over the Enterprise, a group of Ferengi kept the ship's children in classroom 7, including the temporarily child-bodied Captain Picard, Guinan, Ensign Ro, and Keiko O'Brien. A computer terminal in this classroom allowed the team to plan the rescue of the ship. (TNG: "Rascals")
Deep Space 9
Keiko O'Brien opened a school on Deep Space 9 in 2369. Early students included Jake Sisko and Nog. As time went by, more students joined her school, with a total of eleven students in her school later that year, and then later on around fourteen. O'Brien placed the school chairs in a semi-circle around the module when she opened her school. (DS9: "A Man Alone", "Dramatis Personae", "In the Hands of the Prophets")
Several weeks later, Keiko went on a trip to Earth, leaving her husband Miles in her place as a substitute teacher. It was while he was doing so that he advised Benjamin Sisko to separate Jake from Nog, telling him that the Ferengi youth was a bad influence. (DS9: "The Nagus")
A school was to be constructed on Melona IV in 2368, right next to a hospital and residential pods, but the colony was devastated by the Crystalline Entity before any structure could be built. (TNG: "Silicon Avatar")
In 2370, Gul Dukat claimed that the Cardassian education system was "unparalleled" in the Alpha Quadrant. By the age of four, Cardassian children are placed into intense mind training programs, which trains them to have photographic memories and the ability to resist such mind probes as the Vulcan mind meld. They believe that "education is power" and that "joy is vulnerability". (DS9: "The Maquis, Part I")