After high school, you'll need to complete a bachelor's degree, and usually a specialized teacher education program, which often includes student teaching. The bachelor's degree will typically be in the subject you wish to teach (e.g., history, mathematics, science) *or* in education with a focus on a particular subject.
In short: while a high school diploma is the *entry-level prerequisite* for *applying* to teacher education programs, it's far from sufficient to become a secondary school teacher. You need a bachelor's degree and often additional certifications or licensure after that.