Having helped start a similar school (a boarding high school focused on ethics, environment, & innovation), I can tell you that the steps involved are similar to starting any business, though a school will give you a few unique questions to answer first:

•Will you operate as a charter or independent/private school?
•Will you organize as a for-profit or not-for-profit entity?
•Will you deliver instruction in person or on-line or blended?
•What grade/age levels will you teach?

The answers to those questions will then drive both the logistics of where to start as well as much of your high-level business strategy planning. For example, if you're planning in-person instruction, then your start-up strategy must be driven by demographics, as outside of elite boarding schools, bricks-and-mortar schools are largely location-based plays.

Beyond that, I think you can adapt a startup methodology like Lean Startup or Disciplined Entrepreneurship to provide a framework for testing your assumptions and moving your idea forward. I'd recommend starting by creating a Business Model Canvas that answers the basic business questions, including target market, unique value proposition, revenue (tuition) model, cost structure (teacher salaries!), etc.

I'd be happy to help you think through a startup plan, so feel free to reach out. Good luck!