This is an incredibly complex question, which really requires a much longer answer than I can provide, but I will try and shed some insight.

Being published comes down to two approaches. Do you want to publish books for a general audience (like 1776 by David McCullough) or books for an academic audience (college students and professors)? To publish books for a general audience, well that's considerably easy. McCullough has no degree at all in history, but has been a multiple NY times best seller. The problem that I (and many historians) have with his work is that it often has glaring issues and incorrect facts -- but hey, it doesn't matter from his perspective because he isn't held accountable by other historians or by his publisher.

On the flip side, if you want to get published in the academic sphere, well that's a heck of a lot more complicated. There are two main ways of being academically published, peer-reviewed articles that are published in academic journals (like The American Historial Review) or you can publish a book through university presses (like the Oxford University Press). Both these routes are considerably more difficult than getting published in a typical publisher who caters to every day people. Your work will be held to the highest scrutiny you can possibly imagine.

You will need to find and create a piece of literature that presents new arguments, new sources, and new perspectives in your field. The writing needs to be top notch and it need to withstand the critiques of published historians that will review the work (that's where the 'peer review' part comes in). They will provide anonymous feedback to you, through the publisher. you are likely to be fact checked, at least partially, and they will really dive into the question of "what is the new information you are bringing yo this historical conversation with your origional research?"

Now, just being honest with you, it's nearly impossible for any undergrad to get published with either of these outlets. Not impossible, just highly unlikely. I'd recommend talking to your department and seeing what original research you could work on while in school now, but be aware that the skills needed to conduct, analyze, and interprete sources is a skill that takes years to cultivate, and one that graduate school almost certainly needs to help you grow. But you should start preparing for it now.

What is your chosen field? Are you set on it? Find out what are the premiere Peer Reviewed journals in your field (for instance, my master's and speciality is in the American Revolution, and one most respected journal is the William & Mary Quarterly"). Read them. She was is popular right now and talk to your advisors and professors in your field. Find out where the research is going to. And most of all read. Read academic book reviews (in journals) of books that are recently published in your field and see how these historians used their sources to argue their points. If you are interested, I can also recommend a few pieces of reading material to point you in the right direction.

I don't want to discourage you but you are unlikely to get published as an undergraduate as you haven't yet developed the necessary skillset or knowledge to develop a novel research paper. However, it is possible. You need to develop your essay writing technique, develop your knowledge base, and develop your research skills.

Once you start to feel comfortable in these skills, which I would expect to take at least a couple of years, you should find a topic which really interests you and is very relevant to what you have studied. You will need to read everything there is to read on that topic and make sure you aren't asking a question that has already been totally answered, without at least taking a new approach. Once you have written such a paper, you can submit it to a student journal, and it may be accepted.

I should add that you don't need to be published as an undergraduate to do a PhD. When you're doing a PhD, nobody really cares that much about your Undergraduate work, and you won't either, because it's a much lower quality than your work will be as a postgraduate. I wouldn't worry too much about publishing as an Undergraduate. Just develop your knowledge, develop your essay-writing, develop your research skills, and stay humble.

The best advice that anyone can give you is to talk to the professors that you have strong relationships with and follow their advice.

Your university likely has an undergraduate journal, either specifically for history, or more generally for undergraduate research across disciplines.

One caveat, it is not necessary to have actually published to get into graduate school. And it can be a handicap. You don't want to have something that is embarrassing running around ten years from now that gets brought up in a job interview. And trust me, your views will evolve quite a bit between now and potential PhD completion. I know people who wish things from the third or fourth year of their PhD research hadn't seen daylight.