Having an article published is like having a baby. The conception of the article is (usually) an enjoyable experience, but the effort needed to get it out in the open is often gruesome. And the waiting takes about nine months. I can tell because I have some experience in that area (birthing articles, not babies).
The first thing you do to have an article published, is to find a publication that matches the subject of your article, which is the easiest part of the entire process. When you find such a magazine or web site, you will spend some time tracking down the email address that they tell you to use for submitting new articles. This takes about a week, since such a contact page is usually hidden five levels deep in the site, obscured by lots of advertisements and an arbitrary number of dead links.
The email address you find in the end will usually be accompanied by a nice text inviting you to become an author by submitting your article. But don't be mistaken, many of them don't really mean that. When you send your article to this email address, it will usually be ignored for at least four weeks. Make a note of the date of submission and send them a couple of reminders one, two and three weeks after that. Note: some will simply ignore everything that you send them, even the mail bomb and truck load of viruses that you will send their way after having been ignored for more than a month. Just try to forget about them, and focus on the remaining ones.
Fortunately, some magazines will answer your desperate emails and they will tell you they are willing to consider publishing your article. But don't believe them straight away. This may simply be a ploy to get rid of you, because they will now direct you to a web page that describes the format that your submission must adhere to. This page will instruct you to use the least readable font, in point size 11.25 and double-spaced lines, margins of 2.85 inches, and no formatting whatsoever. The file format can be Microsoft Word 6.0, but plain ascii text is prefered. Any figures and tables must be inserted at the most inconvenient places, either at the top, the bottom or at the back of the document, or in separate files. And don't forget to use the proper graphics format, which is the one that is most likely to render your carefully drawn diagrams near to illegible.
After spending about a month reformatting your article to make it follow these guidelines, and re-submitting it to the editor, you will enter the review process. The person reviewing your 1500 words will need at least a month to do so. But most likely they need as much time as global warming needs to pass us over, setting the stage for the next ice age.
Still, despite this lengthy, cumbersome and painful process, everything may turn out allright in the end. And when that newborn article is finally delivered into your own hands you will have forgotten all those awful minutes, days and months that preceded that glorious moment.