How do I correctly design a many-to-many relationship in SQL

You will need to introduce an associative entity in the middle. The associative entity should have the primary keys of the other two M:M entities as its own concatenated (i.e., composite primary key). In short, in all relational database systems, we need to decompose a M:M relationship to two 1:M relationship, getting three tables (instead of two). For example, suppose that a student enrolls in many classes, and a class has many students. In this case we need to design three tables: student (sid, sname, blah, blah); course(courseNumber, title, creditHours, blah, blah), and most importantly the Enrollment table with (sid, CourseNumber, semester, year, etc.).