Qualifications
Do you want to coach a high school sport? Awesome! You're in!
Okay, so it's maybe a little more complicated than that, but not much. If you're already a teacher and you're looking for a way to supplement your income, and if you've played or coached a team sport in the past, then you're eligible for most high school coaching jobs.
Landing a college coaching gig requires more work, especially if you're looking to make your mark in a popular sport like football, basketball, or baseball. You're going to need a bachelor's degree in a field like fitness and nutrition, sports management, or sports coaching. It's also helpful if you actually play the sport you want to coach in college, although you aren't required to be on the best team in the country, or even on a team anyone's heard of.
Once you've graduated from college, it's time to acquire some college coaching experience, which means finding a graduate assistantship. You'll want to get in with a coach you admire at a school with a decent program in the sport you'd like to coach. Keep in mind that you'll be earning a master's degree during your assistantship tenure.
After completing your graduate work, you're qualified to look for a gig as a coach. While you may actually be eligible for some head coaching positions at smaller, lesser-known schools, you'll probably want to pursue assistant coach positions at larger, more competitive schools, where you can acquire the kind of experiences and opportunities that will launch you toward top-level coaching positions.
The qualifications for professional-level coaching differ depending on what sport you want to coach. Approximately half of today's Major League Baseball coaches are well-known former professional baseball players (source). In the NBA and the NFL, some coaches have had professional careers, while others came to their jobs via college coaching.