How does one go about getting something published in High School?

Since you want them published in a paper or something like this you need to talk to the editors there and give them your material then see what happens.
You could write good pieces and still they can decline your work because it’s not suited or just give other reasons.

Better talk to them first and see what’s more appreciated so you won’t work on other pieces.

[ this because you want them published and not write just to have them ]

I suggest you read some good articles as more as you can.

@Hibernate You mean talk to them in person, or would a letter suffice? This is entirely on a whim. I honestly don’t have enough interest in getting published for money as of right now to put forth the effort to write things specifically to their desire. I’m going to write what feels right to me because I lack enough experience to write about a lot of things well and I’m more interested in just knowing if I can by writing what I enjoy writing.
@lovelyleo What type of articles?

In the same way as anyone else @ddude1116. Your ages shouldn’t prevent you from writing publishable material. Do as suggested here and look at publications you like and see if they have any guidelines for contributors. Look at the type of work they publish and see if you can identify any common traits/the quality etc. I would say poetry would be one of the more difficult areas to get into, but if you do a search someone put up a post with websites where you can get your work published online. It was in response to a question asked by @Fiddle_Playing_Creole_Bastard.

Certainly don’t let your age deter you at all though. The more you write, the more you send off, the more you are likely to get published. I am sure there are writers here who can give you more specific advice though.

If you have a good English department at your school, ask your teachers about competitions you can enter or literary magazines you can submit to. Anything that encourages you to complete a piece.

Around here, which is rural, sparsely populated and friendly, you could submit a piece to the local bi-weekly newspaper. If it is readable and moderately interesting, the editor will publish it.

If you’re a good writer, reliable, and filled with ideas, you could write a weekly or monthly column in said newspaper.

What sort of publishing? Are you trying to get it published into a newspaper or literary magazines, or publish like a book would be published? Would it be something you want to copyright? Would it be something you want to sell?

The answer to your question really depends on your answers to the above questions.

If you want to publish into a magazine, all you need to do is find a magazine that publishes literary works, and submit yours. The more local, the easier it is to get it in the magazine. Magazines that publish literary works generally have a limit on the size of the work, and may or may not reserve the right of editing your work. I have gotten poems published this way, and it is very easy as long as you know where and how to submit it.

If you want to publish it as a book would be published (actual publishing, such as you would do if you want to sell copies of the work), the process is much more complex. You have to find a publisher that will publish your work. Many publishers will not even look at your submission if you don’t have an agent. Agents cost money, and don’t guarantee that your work will be published. If you do get a publisher to accept your work, you can expect them to take a large part of profits from the sale of the work, along with many of the legal rights to the work.

If you do not find a publisher, you can publish the work yourself. You can keep all rights and profits, but you have to do all of the work of finding a place to print the book and a place to sell the book. I would not recommend this unless you think that it is worth the trouble.

Even if you do not plan on publishing the work, it is still possible to copyright the book, but it does cost money.

I hope this helps.

@ddude1116 I don’t recall getting money for things published in high school papers. If you want to get them published elsewhere then that’s a different matter.
It’s always better to talk to people in person then to write letters. [ my point of view ]

Have you considered Kindle? Amazon also “offers” Create Space: a one-off, print on demand service. Depending upon a number of issues you may make 30 -70 % of the sale price. It will cost you nothing except time. Check it out on Amazon.com Some folk are doing quite well with it and there are no “door-keepers” as with publishers. Best of luck.