Your question is very broad for this site. I will try to do my best to give you an overview, but you should really ask a more focused question if you hope for more specific answers.
Generally, what opportunities for research grants there are depends on many factors, but foremost where you are geographically and which career stage you are in. Geography matters because most basic research funds are national funds, that is they specifically fund research conducted e.g., in the US, in Switzerland, in the European Union, etc. The career stage matters as most "normal" project grants are available only to people in a certain career stage or position, typically faculty (sometimes also postdocs). For more early-career researchers, other special grant types are often available, such as PhD project funding, young investigator's grants, or similar. However, these usually differ from regular grants in that they often need to be applied for in collaboration with a faculty advisor, mentor, or host. One of the functions of this mentor is to make sure that the grant money is used correctly.
I imagine being at the undergrad level is a problem, but I'm asking for general information - if I have to wait until I'm in a doctoral program or I've finished it, that's fine.
You are likely correct. As an undergrad there may be very few opportunities to apply for grants in your own name. Very few undergrads are academically mature and well-developed enough to form and implement their own research agenda, and giving out grants to students in such an early phase of their career will often be seen as too risky from a funding agency's point of view. Even being a doctoral student is already quite early to apply for project funding in your own name. Most grant opportunities open up for you when you are faculty at a research institution.
To give you one example from Switzerland: most funding provided by the SNSF (Swiss National Science Foundation) is given out through their individual project funding scheme. There are many restrictions on who can apply, but most importantly you need to be working at least 50% of your time in a research-active institution in Switzerland, and you need to hold a PhD degree since at least four years or hold an independent research position, e.g., be an assistant professor (Chapter 2, Article 4).
Your own salary cannot be funded by such a project grant, so it's only used to cover e.g., PhD students that you advise. This also clarifies why the SNSF largely restricts access to these funds to professors - the applicant needs to be somebody who can provide guidance and formal advisory to the staff employed in the project, and they assume more junior researchers will not be able to do that.
In general, how difficult is it to get a research grant? There's relevant data that hasn't been explored and I'd be interested in doing it.
This depends on the grant, but in general it is very difficult. Most grants worth applying to have acceptance rates below 10%. Interestingly, the SNSF project funding scheme mentioned above is an exception, with acceptance rates in the 40% to 50% range
Further, and this is another reason why you may have to wait until you can run your own project, a large part of the grant evaluation procedure is usually an evaluation of the Principle Investigator. Quite frankly, a funding agency will look at grants by established senior researchers much less critically than by academically young or not yet established ones. While this may appear unfair, for the funding agency it is just much less risky to give money to a person that has already successfully conducted many projects than to somebody who hasn't.
Also, how would I go about obtaining the grant? We can define what makes me a good candidate, but then where do I go?
This is not a question that can be answered with the detail that is provided. My suggestion is to keep your ideas in your head, maybe work on them in your free time or as a side project, and then revisit them once you are in the right career stage to apply for your own funding. This will also have the advantage that you then already have preliminary results during the application phase, which is another factor that you can use to tremendously increase the chances of your grant application.