I have a little experience with this...
I graduated in 1985 and have taught everything from 1-graduate school in New Hampshire, Connecticut, Virginia, and New York.
HS teachers generally need to have a dual major: education pedogogy and what ever subject they teach. (For example, I have a degree in English and Education). They would need to take methods for teaching their subject and do student teaching. Most states at that time required the NTE, National Teachers Exam, although a lot of states now have their own teacher tests.
Because it is difficult to get HS teachers in certain subjects (even back in the 80's), a town/city might have been able to hire a math or science teacher that didn't have the educational background. They would give them emergency certification and then require them to take the courses and get a Masters in Education.
Hope this helps. Let me know if you have any other questions.