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When I was fresh out of college, I worked with someone who had their Ph.D who I'll call X. They told me that they had lunch with a person from Facebook who had told them about a Novel Algorithm Facebook had created. X decided to do a patent search on this algorithm, and it did not exist. Therefore, X decided to patent it himself as a System and Method.

My researched solution to a problem could potentially be worth millions of dollars. I don't mean to sound braggadocious or grandiose, but I have experience in the industry, and I'm aware of how potentially valuable it could be. I was thinking about doing a Ph.D on it. How do I prevent professors such as X from patenting my solution, or presenting it as their own idea in a publication? Since my solution could potentially be worth so much money, should I just patent it myself? The only caveat is that it is super expensive to do that. Should I apply for a grant on grant.gov? Should I write a manuscript in arXiv.org? Should I try to write a business plan and try to get funding?

Let me describe fairly typical practice at reputable US universities. When someone has a patentable idea, the university itself will take over the patent process, paying lawyers and fees. The university will probably be the patent holder of record, but will make arrangements with the actual creator(s) to share any income that results from exploiting the patent.

This can be good or bad, I suppose, but the good part is that the university covers the cost and also provides backup if anyone challenges the patent at any point. This can be very difficult for an individual to do on their own. The bad part is that the patent is probably in the university's name, though that may vary. Another point is that the university may take it upon itself to find ways to monetize the patent if it is awarded. Again, this can be a large expense for an individual.

But one protection for you, a student with an idea, is that if the university is, indeed, reputable, it won't try to steal your idea or let a faculty member steal it.

But faculty at the (reputable) institutions that do a lot of patentable research normally require this (or a similar) process as part of the contract with the faculty member. Such agreements might also be necessary for a student to participate in such work. And there is usually an office, full of lawyers, dedicated to shepherding such work. So a further expectation is that the university is not only reputable, but also large enough to support that office.

And the sharing arrangement may be standardized or, possibly, negotiated, so long as costs can be expected to be covered.

The situation and the rules will also probably vary by a lot in other countries.

For completeness, I'll note that large companies doing important research also tend to have (and require) some similar arrangements with their own researchers.

About doing a PhD, before thinking about academics stealing your idea you might want to think about how you are going to publish papers (usually a requirement during the PhD) if you want to keep your idea secret. As far as I know you won't be able to publish anything before the patent is granted, and that could take a few years. It doesn't mean that it's impossible but it might be tricky.

The alternative to the academic route described in Buffy's answer is to create your own start-up first, then develop and patent your idea under the name of your company. This might take a few years and will cost a lot of money indeed. If you can make sure that your idea is viable and really worth millions of dollars, then it's still a sound investment.

The first step would be to consult with a good specialized lawyer who will advise you on how to proceed (for instance inform you about NDAs, you will probably need these). Again, it's worth the expense in order to avoid making mistakes which could easily ruin your business.

What you describe is closer to "scooping" than "patent trolling". But actually it's just theft.

If you truly believe your invention is valuable, then you can patent it yourself. You would need to find a reputable patent lawyer. And you can expect to pay thousands of dollars in fees. (Beware of disreputable patent lawyers.) Plus you will likely need the help of lawyers again to actually collect any money from your patent, as you must sue those who infringe on your patent, or at least threaten to do so.

If you just want credit for your invention, write a paper about it and stick it on arxiv or a similar repository. The arxiv timestamp clearly establishes precedence. That means no one else can subsequently patent the invention -- your work becomes prior art that invalidates any subsequent patent. Sharing your invention like this does not immediately prevent you from patenting it. However, there are time limits. I believe you need to submit a patent within one year of making it public.

Note that your employer may claim ownership of any intellectual property that you create. For example, most universities do this. On the positive side, this means they may pay for the patent. On the negative side, they may claim some or all of the money you get from it.

I was thinking about doing a Ph.D. on it . . . "

I think the first question is for yourself as a person.
Which human environment do you prefer to work in ? The business environment or the academic environment ?
This is the essential question here as people in these two sectors relate and associate in completely different ways.

If you have the urge to impart and receive knowledge freely, are comfortable in situations of psychological trust with young people and not too worldly when it comes to money, maybe a Ph.D. with the right supervisor is a valid consideration. If you go this route, don't expect to be rich. Staff at colleges sometimes make millions from their work but no student does - unless the insights are kept secret and developed later off-campus.

But don't go into a Ph.D. just to experiment/develop an idea you want to commercialize. Campus life - and the kind of people there, good and bad - will find you out, drain your confidence and leave you feeling socially isolated. For the rapport, team-work, thrilling intensity and chillouts - these are the preserve of the private sector where the necessity of making a living fuse people's mind together. Patent trollers are a natural hazard here but you'll have support from your own company and many patent attorneys will undertake protection work on the understanding of later payment after patents are granted.

Edit: Sorry, misread question. Salvaging what I can of it.

It's best not to get too carried away with the commercial potential of new ideas. It's one thing to come up with something, but something else entirely to connect that to a customer who will pay more than it cost you to develop it. And then there's the possibility that Facebook and others already know about it and are treating it as a Trade Secret. In the latter case your patent may not be worth much at all and could potentially be overturned in court.

I'd suggest thinking carefully about what your business plan would be, who your potential customers are, and how your product would be used by them. Would they license your IP? Would you work as a consultant to implement it on their systems? If the idea is just to "make millions" simply positioning yourself as a gifted developer who independently discovered X could be enough to get your foot in the door of some very high-paying firms. Or to put it another way, you may be worth a good deal more than your patent.

For Universities, policies will vary from place to place so you should consider consulting them directly. In Australia students generally are not required to give up their IP, but can voluntarily do so in return for some royalties and the University footing the bill for patent applications and legal protection of said patent. You'll need to assess for yourself whether the trade-off is worthwhile.

And finally, if you're worried about being scooped by Prof X then I'd strongly advise #1 not telling him and #2 documenting the development of your idea in a way that would be independently verifiable in court if necessary.