What should one do if they've discovered a "breakthrough" but lack academia credentials? Let's assume someone has a very thorough knowledge of a particular field of science but they have absolutely no formal education in this background.

This individual one day realizes a very novel approach to solving a somewhat complex problem.  After developing independent tests and coming up with rock-solid evidence that her method is groundbreaking, and consistently produces test results that would be impossible without a legitimate solution, what can she do with her research to both share the information with the world and retain some form of credit for the discovery?

In other words, how can one be both a hobbyist contributing to a field of scientific study and yet also retain the respect they deserve for their work if it is of great use and benefit?

To be clear, this isn't about having one's name appear in a Science Journal without the necessary credentials.  I think it's respectable to maintain certain sets of rules and standards for journalistic publications.  However, it also isn't fair for such a person to have to divulge this information to someone who is "qualified" and have them receive all or most of the credit for someone elses work, just because that other person hasn't earned a piece of paper.

How can hobbyist both share, and maintain, the recognition they deserve if they make a legitimate scientific breakthrough?
I see a few approaches you could take (or some combination):


Write up the idea as a white paper and submit to http://arxiv.org (or something similar). This gets the idea documented, public, timestamped, and allows people to easily cite it.
Reach out to researchers in the field to see if they would be willing to help you form a scientific paper based on your idea. Not all professors are scary!
Submit to the industry track of a research conference if you have an industry background (if not, then maybe a workshop). Some conferences elicit papers from industry that can get your idea out there, generate discussion, and allows you to get feedback. These tracks are often less competitive and very open to non-researchers. For example, Software Engineering In Practice at the International Conference on Software Engineering