Now that you've contemplated those questions, let's get back to the "how". For that, I direct you to, "Steps for Starting a Nonprofit Business" by SCORE. Of course those steps are just the tip of the iceberg, but, if that article was helpful, check out SCORE's many other resources about forming a non-profit (just type "nonprofit" in the search bar).
Which leads me to talking about SCORE - an amazing resource for any person wanting to start a business. SCORE is an all-volunteer organization, providing free (and confidential) mentoring to help start or grow businesses. The Champlain-SCORE chapter serves Vermont with branches in Burlington, Montpelier, St. Albans, Middlebury & Rutland. But you don't have to go in person to use its services since it also has online counseling for new and existing businesses! Additionally, it offers workshops, seminars, and webinars covering a wide range of topics from how to write a business plan to marketing to business valuations. Its been around for 25 years and has assisted over 5,000 Vermonters in starting, running and growing businesses.
Hopefully this will get you started in answering the question, "How does one start a non-profit?" as well as introducing you to SCORE. However, please realize that all of these resources are just that, resources, and not meant as legal advice. Requirements may vary depending on the type and where you want to locate your nonprofit. To fully understand everything you need to navigate and be aware of, consult with both legal and tax professionals before moving forward. Cheers!