Explore your article topic. Determine what you would like your argument to be; generally one argument has two opposing sides, one for the topic and one against the topic. Both are needed to write a well-rounded discursive article.
Gather evidence for both sides of your argument. Search for credible information within books, academic journals and scholarly online sources. Gather the same amount of evidence for each side of the argument so that your article will not appear biased.
Write your introduction. The introduction is generally a paragraph long and should discuss the article topic and the two opposing arguments in general. Include facts about the opposing sides.
Write your body paragraphs. There are several different approaches to this process, one of which is to dedicate a body paragraph to each of the evidences found for the opposing sides of the argument. Use either the A, A, B, B format, which means that all of the evidentiary paragraphs for the first side of the argument are grouped together, or use the A, B, A, B format, which means that the evidentiary paragraphs alternate from one opposing side to the other.
Write your conclusion. This should be one paragraph in which you briefly summarize the main points of your discursive article. Write which side of the argument you find to be more factual or more accurate and why, based on the evidence you present in the body paragraphs, you find that to be the case.
Check the grammar, spelling and content of your article for accuracy and logic.