Define your argument. Be specific. If your argument is too broad, you will probably have a difficult time finding a rebuttal that speaks directly to your argument. For example, if your argument is "fast food is bad," you will probably find too many rebuttals, such as "fast food tastes great." Instead, argue that fast food does not have any positive health benefits, which will likely provide more specific rebuttals.
Conduct a survey of your peers, coworkers or professors. Present them with your argument, and ask them whether they agree or disagree with your argument. If any of them disagree, ask them why. This process will give you a good idea of what topics to research. You can also use this information as a rebuttal, depending on the formality of your paper.
Conduct research at the library and online to find out what people are saying about the topic of your argument. You will want to look for scholarly articles from journals or books by subject experts. You will likely find many different theories about your argument, so make sure that you choose the rebuttal that most specifically relates to the position of your paper.
Record all the information that you will need, such as author, title and publication date of the sources from which you take your rebuttals. If you are going to paraphrase someone else's argument to use as a rebuttal, you will need to give that author credit by providing a Works Cited page. Depending on the style you are using (e.g., MLA, APA, etc.), you may also need to include in-text citations.