What steps would an amateur scientist have to take in order to get a scientific breakthrough published? I would like to know from an academic standpoint on what steps that an amateur scientist would have to take in order to get his/her scientific breakthrough published in a major academic journal/scientific magazine.

Say that this person is outside of academia, he/she has no college degrees, and he/she has stumbled upon a scientific breakthrough by chance after years of doing self-study, research, and experiments with a particular scientific area of study.  Also, say that this person has a job with a modest salary so if they will need to raise a lot of money to get it published, they will have to get it from an angel investor or from crowdfunding. 

Although I understand that the odds of such a person coming up with a scientific breakthrough is very slim to none, I still would like to know the process that this person will likely have to follow if he/she wants to get it published.

For example, would the first step be that this person should take be making an appointment with a college professor in order to get a professional opinion on their scientific breakthrough?  If so, what guarantee does the amateur scientist have that this college professor will not try to steal this scientific breakthrough?  Should the amateur scientist insist that the college professor first sign a Non-Disclosure Agreement?

Would the second step be that the amateur scientist meet with another college professor to in order get a second opinion and again have that professor sign a NDA?  What would be the 3rd step, 4th step, etc., etc.

Although there are probably many steps in the process of getting it published, I'm interested in just the major steps that will likely have to be taken.
The title question is answered by "write a paper and submit it to a journal". The amateur scientist doesn't need anything special to do that.

The questions in the text deal with a separate question, which is whether or not the breakthrough actually is a breakthrough. In this case getting a professional opinion is certainly going to be helpful (see Kaveh's answer to a related question for the process). It's easy to deal with the "threat" of the professor stealing the idea: just establish precedence by, e.g, attaching the manuscript to an email with a timestamp. If the professor tries to steal the idea anyway, he would be breaking some deep-rooted academic norms. If it's proven that he's plagiarizing, he can get into serious trouble.