Qualifications
Regulating education is generally left to the states, so there's no hard and fast rule for qualifications to be a sub. There are a few states that'll let you sub with just a high school diploma. Much more commonly though, school districts will require subs to hold a bachelor's degree. The field of study isn't important.
After all, you're filling in for everybody regardless of subject matter—you really just need to be an expert in children not dying while you're around.
You'll likely also either have to pass a basic educational skills test or take some sort of pre-service training. The requirements are rarely stringent—districts just want to know you have the basic knowledge to talk to a room full of kids for forty-five minutes at a time.
In California, for example, subs are required to pass the California Basic Educational Skills Test (CBEST). This tests for high school level reading, writing, and math ability.
Alternately, in Kansas, subs are required to complete a ninety-day teacher education program. It's unknown if you need to have a high school proficiency there, but one can hope.
You'll be asked to pass a criminal background check as well, and get up-to-date vaccinations. You're in a school with kids, so you can't be passing out the measles along with the assignments their teacher left.
Generally, though not always, subs will interview with a school administrator before being placed in a classroom. Preference in sub hiring will usually go to subs with past experience—trust goes a long way in this line of work. But if you're just starting out, it'll be important to show enthusiasm, confidence, and flexibility. If you can show some background experience working with children, it'll also help your case.
So get a bachelor's degree, have a clean record, a good bill of health, and demonstrate to the hiring school administrator that you're up for a challenge, and you'll be well on your way to earning a little bit more than minimum wage.