What research in theoretical physics could a high school student do? I already know what  I want to conduct my research on (topic: magnetic monopoles), the problem is just that I don't know what to investigate or analyze. What are some research methods you would recommend? What are some easily applicable concepts? Preferably, rather advanced topics/math, but "simple" execution.
To be clear, I am not interested in specific examples of what I can do, but rather a more general description of how I would be able to come up with something useful that I can use to conduct my research.
 A: To do research is to go into territory that is either not-yet-entirely-charted, or at the most challenging end of the spectrum: uncharted territory.
The uncharted territory is at the periphery of the body of knowledge that the physics community has amassed. Over time students of physics have to cover more and more ground to eventually arrive at the periphery, where the available maps show mostly white areas.
However: there are also small whitish patches in nearby territory:
One example of a that, in my opinion, is the Dzhanibekov effect
I recommend the following article by Nicholas Mecholsky:
Analytic formula for the Geometric Phase of an Asymmetric Top
And the following video by David Brown:
The Dzhanibekov Effect: Equations and Simulations
This is not a suggestion to you to take up those subjects, I'm mentioning this to show that nearby too there are still new insights to be had. Not necessarily new discovery, but new clarity, deeper understanding.

There are a lot of attempts out there to explain the Dzhanibekov effect, and there are noticable differences. That means that those people do not actually understand it as well as they think they understand it.
(Nicholas Mecholsky and David Brown do understand, which is why I recommend them.)

We now live in the age of internet connectivity; information is accessible at a level and speed that is far, far beyond any level ever in history.
I very much believe there are possibilities.
I believe there are opportunities for discovery nearby.
For sure, you will have to be very attentive. Look voor areas where explanations that are given are a bit fuzzy.
Possibly you will find an area where there is still some new understanding to be found.
A: If I were you , I would search colleges and study for good grades in High School which would put me in a good college  instead of doing research on my own in physics.
But if you want to do research on your own I suggest before the research to study the basics about the subject of research.I would probably pick something which I have access to devices which can perform my experiment.
In order to search for magnetic monopoles you need a particle collider which isnt something regular people have access easily.
