I don't know how to copyright a video game idea.
I don't know if I should make a game document and get that copyrighted first or make the game then copyright it.
The main gist is.. I am lost.
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You're confusing patents, copyrights, and trademarks here.
Without going too deep into details:
Whatever you create, code, assets, or anything else, automatically has you as the copyright owner. No further actions required. It just has to require significant amount of work (depends on legislation). For example, you can't claim rights on blue rectangles, but a logo consisting of multiple rectangles.
Trademarks are protected logos, taglines, etc. Like patents, but not on ideas.
Patents are protected ideas, e.g. to prevent others from profiting off things you've put lots of time, money, and research into. Sometimes they're just trolling stuff though.
The copyright and trademark symbols, i.e. © and ™, are really just hints. The © informs people that your work is protected by copyright, and the ™ informs them that you are using a name or symbol as a trademark. Even without them, stuff is yours. It just makes it harder for others to claim they didn't know about these being your trademarks or property. (Some jurisdictions might require them, though.) In contrast, the ® symbol is restricted to trademarks which have been registered with a governmental trademark office. These trademarks have a greater degree of protection, since they've been reviewed and approved to determine that they're unique or distinctive.
So, if you write a game or story or whatever, you don't have to do anything. You might want to file a trademark with the title or main characters, but that's it. If you've got a new way to interact with the player or do something special, you might be able to patent it, but that's really on a very specific case by case basis.
Usual disclaimer: I am not a lawyer and in this site questions about these issues have to be always taken as ideas, thoughts or experiences, never as technical advice.
That said, in the US you hardly would be able to copyright (or hold a patent over) a game idea in itself. Actually, the US Copyright office says that:
Copyright does not protect the idea for a game, its name or title, or the method or methods for playing it. Nor does copyright protect any idea, system, method, device, or trademark material involved in developing, merchandising, or playing a game. Once a game has been made public, nothing in the copyright law prevents others from developing another game based on similar principles. Copyright protects only the particular manner of an author’s expression in literary, artistic, or musical form.
Of course, this is a bit too vague. Consequently, the interpretations at the Courts have been diverging a bit. There is an excellent article on Gamasutra, from 2013, that discusses that: "Clone Wars: The Five Most Important Cases Every Game Developer Should Know". Still, it's quite the standard that game ideas are not patent-able per se.
What you might be able to do is:
Besides that, what you can surely do is:
trademark game titles, logos, characters, etc;
copyright the assets (art and sound) as audiovisual. Note of caution: while you don't have to copyright them because once you create those you own them, yes there are quite a few arguments in favor of specifically filing copyrights on them. For more on that, see the other question on this site: Questions on the legal protection of games and their parts (assets, sounds, title)).
Lastly, take a look at the article ["Video Games and the law: Copyright, Trademark and Intellectual Property"] for further detailing on the matters of game trademarking and copyrighting.
: https://www.newmediarights.org/guide/legal/Video_Games_law_Copyright_Trademark_Intellectual_Property# Are video game titles copyrightable?