You can notarize documents with your idea (this can confirm priority if no one has come up with this before). To protect intellectual property, you need to get a patent - the patent office will evaluate the novelty and patentability.
Fortunately or unfortunately, you cannot patent just an idea on something - in most industrial countries patent laws stipulate that it has to be a "technical solution" with certain degree of novelty.
That being said, recently I have seen many discussions about the inadequacy of current patent system, when instead of promoting innovations it blocks it.
One way to establish your authorship on an idea would be to publish a research paper (if you are talking about a scientific idea) on this particular subject; in experimental sciences (like chemistry for example), the idea better be supported with some data proving its viability.
You need to prove anteriority: that you are first to propose your idea (a concept with a system design would be better, as explained by previous contributors).
There are two mechanisms, depending on your intention:
-academic
Submit an article to a peer reviewed journal. The reviewers who are recognized in the field will confirm the anteriority, originality, relevance of your results and method.
-industrial
The patent examiner will assess your anteriority, originality, relevance.
An article proves, demonstrates, documents.
A patent describes, justifies, claims.
With an article, you will be quoted in further research by others.
With a successful patent, licensees will implement, go to the market with a system, product, service, and you may get royalties.