Every nonprofit organization starts with an idea that will hopefully change the world; so do and some don't, but each has to go through the necessary steps to start a nonprofit organization.
The most important thing to keep in mind throughout the process is the need to continually do your research. Running a nonprofit is not something you can simply learn as you go. And while you may have to make quick decisions, your success is not dependent on your ability to "wing it," but rather your ability to make well-informed decisions in a timely manner.
That being said, if you're considering starting a nonprofit you likely already have an idea in mind. It's time to develop that idea. What are your primary and secondary objectives? Is this issue one that could be supported by the general population or only by a specific demographic? Are there other nonprofits that already exist in this capacity? How would your nonprofit be different?
Once you start considering the legal and financial implications, it would be wise to get in touch with an attorney - once who has experience with nonprofits - and seek out their input. Their expertise will be a wise investment as you get started; however, many people have started nonprofits on their own.
As you move forward, having developed those objectives, create a mission statement which appropriately encompasses what you hope to accomplish. There are plenty of in-depth, online resources to help you learn how to write a proper mission statement, but keep in mind that mission statements should briefly, yet effectively, define what you organization is and what its purpose is.
A nonprofit should also include a board of directors. These are individuals who can share the vision of your nonprofit, as well as fulfill specific responsibilities toward that end. The number of people on the board can vary (although most states do have minimum requirements) as well as what aspects of the nonprofit each individual will be in charge of.
Working with potential board members, now would be a good time to develop some formal (or, perhaps, informal for now) bylaws that will help govern your nonprofit. You'll also want to begin developing a budget and accounting system, establish a standard for keeping records, and other bookkeeping needs associated with any organization.
Once all of that has been done, a process which could take months or even years, only then should you start with the paperwork. Each state is different and you should find out what is required of your state. You will also need to obtain a federal Employer Identification Number before you officially file for nonprofit status, and the subsequent state and local tax exemptions.
It takes time, but with some hard work and a lot of researching, you should have an official nonprofit organization that is ready to hit the ground running