Write an introduction that introduces the topic to be argued against. Include a thesis statement at the end of the introductory paragraph that expresses an opposing point of view and indicates the alternative perspective for which the essay will argue. The thesis statement only needs to be one sentence.
Write two or three paragraphs providing evidence that opposes the essay title. This evidence must be supported by documented academic study or facts drawn from reputable sources. It cannot be purely your own opinion or opinion taken from anecdotal evidence.
Introduce a second block of evidence to support your argument and write another two or three paragraphs of evidence. Again, this must be documented research that supports the counterargument the essay is making.
Return to the original argument to acknowledge how valid the perspective of that argument is, and to indicate how far you agree with it. Write a couple of paragraphs in this section to show respect for the opposing viewpoint and demonstrate that you have considered the opinion, although you still disagree with it.
Return to your own argument, and write two or three paragraphs that reassert the opposing viewpoint with further evidence or analysis. This is a rebuttal of the initial argument and a reassertion of why your alternative perspective is more reasonable.
Write a conclusion that suggests a new way of looking at the original argument you have been writing against, in light of the new evidence you have presented. Always bear in mind that your objective in writing an argumentative essay is to try to convince the reader that your argument is the more enlightened perspective.