Dnil,
What you really want to do is check out what the requirements are to become a teacher.
Example in AZ. you need a minimum of a BA degree and teaching certification. The two are not necessarily the same. I had a BS in Public Admin and needed to go back to school. I opted for a MA in ED and took an additional 9 units to get my teacher certification.
If you have a BA already I suggest you start looking at being a substiute teacher in the grade level you are interested in. This will give you a worst case scenario environment to see if this is something you really want to get involved in.
There are usually different levels of what school you can teach with a particular degree. The requirements of a particular subject matter are certainly more stringent the higher you go in the system. Example, a degree in biology if you will teach that subject in a High School area but a General Science degree to teach basic science in a Junior High level. In my state the elementary and junior high grades are all available to a teacher with a basic education certificate. For High School you need a secondary teaching certificate. The same for vocational ED like they use in some specialty magnet schools that focus on a particular type of education, music, art, science, aviation, computer sciences and so on.
Subbing is a good way to get your feet wet while you take some courses that may be required for your teacher certification. If you do not have the minimum level of education for subbing look at a school and talk to the principal about being a teachers aid so you can see what it's like. Some school districts have those positions at a minimal pay level (minimum wage) and you get to see how it really is in the classroom while you are deciding to do something else.

In short, talk to some local school folks and get an idea of where you stand on qualifications. Good luck...... you'll need it.