After reading my answer, please follow the link below. You will find a much longer and more detailed answer to your question at that page, which is entitled “How to Write an Argumentative Essay in 9 Easy Steps.”
The first thing to do is to “conceive” of your paper. What that means is that you need to find a topic that can be made into a good essay. In my view, the most important thing about the topic is that it needs to be interesting to you. I have read too many essays that sounded like the writer did not care about the topic at all. This is not good. So, think about what things interest you and then think of an argument that can be had within those topics. The more you are interested in your topic, the more interesting your essay will sound to the reader.
The second step is planning your paper. I would plan by trying to decide what I think the most important points for my argument are. If I do not already know important points, I will need to do some research on the issue. Each of the points I choose will end up being the basis for a paragraph (or perhaps more) in my essay. As part of this process, I would also look for arguments that contradict my own. I always encourage my students to give the other side of the argument. I believe that an argumentative essay is always stronger if it presents the other side of the argument and then defeats it. Once I have the main arguments for and against my point of view, my planning is done and I am ready to write.
Writing is, in a sense, the easiest part of the process. You just write down the arguments against your position and then follow them up with the arguments in your favor. There are a few things that you must be sure to do, though. Be sure to have separate paragraphs for separate ideas. Do not put off-topic material in a paragraph. Be sure that each of your paragraphs has a thesis statement, a body, and a conclusion just like your essay as a whole should have. Try to use transitional phrases or sentences as often as possible. This will allow your writing to flow and to feel more coherent to the reader.
Finally, there is the process of revising. If possible, get someone else to read it. Have them tell you what parts of the paper do not make sense to them. Change those parts to make them clearer and easier to understand. If you cannot get someone else to read your essay, read it very carefully yourself. Make sure that you have clearly explained everything and that the ideas in your paper make sense. Make whatever changes are necessary.
Again, please follow the link below for a more detailed discussion of how to write an argumentative essay.