All right, let's take the guidelines you've mentioned: (a) a cause-and-effect question, say, "Why did X happen?", and (b) the existence of multiple scholarly opinions on the matter. I did one of my secondary school term papers on "Why did the Equal Rights Amendment [for women and men] fail in the 1970s?", so let's use that as an example.

I found three competing perspectives on the matter. (Remember, AskHistorians friends, this is teenage me using pretty much just JSTOR; judge not lest you be judged). (1) Scholar A did a straight-up numbers analysis, looking at population size, delegate total, relationship between legislative schedules in states versus time limits on the national scale, &c. Basically: all math. (2) Scholar B argued it was church-based opposition from conservative Christians lobbying politicians. (3) Scholar C argued that it was a gender issue, that Phyllis Schlafly and other antifeminists basically scared America deeper into sexism.

So my paper begins with three paragraphs/sections (depending on length limits), summarizing each argument and setting out a couple of key pieces of evidence that the scholars raise to support their thesis.

Then I looked for primary sources. A lot of times, these will already be cited in the footnotes of the scholarly articles and books. In my case, I looked at newspaper articles and speeches. You might also use additional secondary sources here, on related topics--like if I had done research on Roe v. Wade (protecting abortion rights in the US, a major women's issue) and the backlash against it. Which I did not, but again, bless me, Braudel, for I have sinned.

I read my sources and picked out key points and quotes, like when newspaper articles were interviews with "person on the street", or if they described a speech with large attendance.

There are two ways to structure the paper from this point. One:

You organize your primary source evidence and lay it out, making your own case for why the ERA failed. You use the three scholarly arguments to help you structure your own gathering of data and how you present it in the paper. You see if you find stuff that doesn't fit with any of them.

Two:

You repeat the initial procedure. You take Scholar A, then posit the additional evidence you found that supports and refutes the case. Repeat with Scholars B and C.

In the end

You draw a conclusion based on your analysis part. Is one scholar right? Are there good points in all of them? Are they all wrong?

In my case, I am quite gratified to see that Wikipedia in 2019 backs up the conclusion that I reached in high school, despite the fact that the only good thing about that paper was probably its title:

"The Politics of Public Toilets."

~~

I hope this helps!

So what I tell my students is this: a (good) historical paper is a paper that asks and answers (to some degree) a historical question. What is a good historical question? That's the hard part. Sometimes the best ones are pretty straightforward and "simple" at their core. A recent paper I wrote is basically trying to answer the question: "What did Truman know about Hiroshima prior to the atomic bomb attack on it?" It's an odd question to ask, but it makes for an interesting answer (almost nothing, in fact he may have thought it was a military base and not a city). A more straightforward undergraduate history question along similar lines might be: "How did the Japanese first understand what had happened after the Hiroshima bombing? What were they told, and how did they verify it?" (This is a question that gets asked occasionally here on /r/AskHistorians — it's a good question!) This is a question of limited scope, unlike, "What role did the atomic bombings have in encouraging the Japanese to surrender?" which is good question but a huge one (entire books are written on it).

Most history papers don't start with knowing the question in advance. Often you start with a general idea of what you're interested in (e.g., "the atomic bombings") and then you read around a bit and try to find something interesting in there. My paper on Truman didn't start with that question; it started with being interested in a contradictory passage in a journal Truman wrote (which said that the first bomb would be used on a "purely military" target and spare women and children, which didn't happen obviously), and then working outward from there. (You could rephrase my question as, "if Truman wasn't lying in his journal, how would he have been so wrong, and what are the implications of this?") It's OK to start a topic without knowing the exact research question, but you need a research interest of some sort. And again, narrowing the research question down to a non-book-length is a difficult trick, the sort of thing one learns mostly through experience/trial and error. Of course you can narrow the question down as you go, as you discover whether it's too easy to answer, or too hard.

OK. So how do you answer a research question once you have it? You look at sources, you look at arguments by other scholars, you try to put bounds on the answer. Sometimes there isn't a single answer — usually there are several plausible answers. That's fine for a history paper; we like nuance. But this is straightforward research work, with the only trick being that you need to know where to look for sources. Librarians can help with this, as can JSTOR, as can Googling. But a useful trick early on is to find any single article or book that is relevant and to look at their sources. If you do this a few times you very quickly become knowledgeable of what the most important works surrounding a question might be, and what kind of sources are used by everybody, which is both helpful because now you can consult said sources/books, but also you know what the limitations might be (if everyone is looking a memoirs, you might ask, are their non-memoir sources that corroborate or contradict these arguments?).

OK, you've got a question, you've got some evidence. How do you write the essay? Here's the big secret: the same way, more or less, you'd write any essay. Just because it's about the past doesn't make it that much trickier. You have to think carefully about the past, to be sure (you need to engage it on its own terms, be thoughtful about what can and can't be known, etc.), but the writing is writing. You have an introduction that sets up what you're doing, you give evidence and go through different angles of the research question, and then you conclude by answering your research question. The paper should ideally flow logically from your question to your evidence to your conclusion.

The actual writing is as hard as all good writing. You need to structure your paragraphs carefully and be aware of how you use evidence. You need to anticipate the kinds of questions that your evidence might raise with the reader, and the kinds of objections that your arguments (the "answers" to your research questions) might raise. You need to cite your sources, and work your way through the argument and its deficits. But this is just the skill of non-fiction writing. The best way to learn it is to try it, and then get feedback from someone who is a good reader, and then take that feedback seriously.

As for the "brain becomes a mess part" — if you find yourself to be a scattered writer, compensate by investing more time in organization. Outlines can help. Some people take very detailed notes and put them in chronological order. Find a strategy that works for you. Because you do have to marshal a lot of information to write a good history paper. And if your brain doesn't naturally hold that information in there, you need a system. (I use databases for the sources, and very loose outlines for the paper structure, myself. If I have a bunch of sources I need to process, at a minimum I make a Word file where I just go through each of them, writing down what jumps out as interesting to me, and then I use that Word file to think about what kind of argument I am going to make. I find it easier to work from notes than the documents or books themselves. But everyone is different. Find what works for you.)

The only other advice: to learn to write better you need to learn to read better. Look at an academic history paper and work out its structure. What's the intro doing? How does the citation and evidence work? How do they deal with long quotes versus short ones? And crucially, how do they end the damned thing? Feel free to mimic the overall structure of the work of others. Someday, when you're good at this, you can innovate and break the rules and etc. But you need to learn the rules first before you start to break them. And there's no better, or easier, way to do this than by using another essay as a structural model.