I hope I can help a little. The requirements for teaching in public schools are set by state law. Thus, you will have to look at your particular state for its rules. Generally, you get certified by having a degree in a subject, the appropriate education classes and pass several certification examinations. Some states have special programs for "fast tracking" people in other careers into teaching. These programs have intense classroom instruction (some as little as 6 weeks). I believe this only allows one to teach for a limited time, so a masters degree in education might be required to continue. Private schools set their own rules, but also tend to pay much less: in some places half.
In NY, I think you need to have a teaching certificate in the appropriate field to get a tenure track job. For secondary education, this requires 36 hours in you field plus the appropriate education classes and the exams. It is possible to get a permenant substitute position, however, which would let you teach without one.
Ed