You need to be licensed to teach in public schools. In all states, getting licensed requires you to have at least a bachelor's degree and a certain amount of supervised practice-teaching experience. Some states also require you to have a master's degree.
In addition, many schools now combine bachelor's and master's degree programs in education so that you graduate with both degrees. This is because many school districts require a master's degree within a certain amount of time after hiring.
As part of their licensure processes, many states require you to take a test to show your competency to teach. This is typically the Praxis series of exams.
Getting a bachelor's degree prepares you to teach at the K-12 level. If you want to teach adults in a community college, or if you want to teach at the university level, you need to earn at least a master's degree as well.
Some programs offer part-time study options so that you can continue to work while you're in school.