A class was a gathering of students who were taught by a teacher. Classes were often held in a dedicated location called a classroom.
In 2151, the fourth grade class of Worley Elementary School sent questions, letters, and drawings to the crew of Enterprise NX-01. (ENT: "Breaking the Ice")
During his time at Starfleet Academy, in the late 2250s, one of the first things Gary Mitchell learned from upperclassmen was that a student either learned to think in Lieutenant James T. Kirk's class, or they sank. (TOS: "Where No Man Has Gone Before")
As a student in Doctor Roger Korby's class, Christine Chapel learned about his unwillingness to harm any insect or animal. He held life sacred. (TOS: "What Are Little Girls Made Of?")