By simple, I mean reasonably practical to put into effect.
I think that unobvious, I mean that, despite the ease of actually using the technique, it requires some careful study and discipline to invent on your part.
I think legal and moral explain themselves.
Assume for the sake of the discussion that the technique is not something that could really be protected by copyright.
Who, if anyone, do you share this technique with, and why?
Absolutely no one. It would devastate the economy.
My partner, because I’d want him to be in on it. No one else.
Seems more likely that the technique would become less effective the more people knew of it.
It occurs to me that I should have been clearer in the OP. The method discovered would be something akin to the things [del]that lying scumbag[/del] Kevin Trudeau pimps in his books.
First of all, tell it to me.
Then, after amassing a nice chunk of change, I would try to do some good things for other people until I found a trusted mentor or two, and would then pass on the secret, swearing them to silence until I am long dead and gone and they would continue to do the same.
Say what you want about Microsoft, but Bill and Melinda Gates have done a damned fine job of ensuring the vast brunt of their wealth is/will be distributed to charitable causes through their foundation.
The IRS. 
isn’t what you are describing essentially a successful innovation/invention?
See Post #4.
Think of all the infomercials in which you’re invited to buy a book showing you how to get secret government money, or make your fortune through real estate, or whatnot.
I would tell nobody, because that would destroy the method. It doesn’t work if everybody knows the method. You can’t achieve beyond the average if everybody does it.
Make so much money it’s a wealth that can sustain generations- then franchise it.
No one learns my secret. I smugly roll around in my millions and entertain friends and family lavishly. Before I die, I prepare an elaborate puzzle and globe-trotting scavenger hunt - the person who successfully completes it will learn my secret to vast wealth. I will, of course, post the starting clues here on the Dope. Good luck!
In case anyone is curious, real-world examples would be trading strategies based on stock market anomalies. The January Effect is a one such anomaly. Quoting from the Investopedia entry (January Effect: What It Is in the Stock Market, Possible Causes):
*A general increase in stock prices during the month of January. This rally is generally attributed to an increase in buying, which follows the drop in price that typically happens in December when investors, seeking to create tax losses to offset capital gains, prompt a sell-off.
…This historical trend, however, has been less pronounced in recent years because the markets have adjusted for it.*
Basically, as knowledge of the phenomenon became widespread, more people capitalized upon it resulting in decreased profits for all. The effect was first noted by an academic, who had a professional incentive to publicize the finding (i.e., academic reputation, tenure, etc.). I suspect there are numerous other profitable market anomalies that have been discovered by researchers at investment companies, and as such are still being quietly exploited for profits.
For a single one-off simple payment of $25 sent directly to my PO Box address I will send by return the secret that led to my astounding wealth and on-going income that has ensured I never have to work again, other than 20 minutes a day sitting in the comfort of my own mansion, and neither will you !
No one. Others would benefit from my wealth, but no one would know the method. As far as the IRS is concerned, I’d be self-employed.