As the assignment materials note, this assignment calls for the use of Aristotelian Argument Format, something that's been around quite some time and is quite an effective matrix or format for just about any paper where you are asked to argue a point. Here's how an argument for this assignment could look. I'm using a topic that is more or less easy for me to layout, so don't make too much of it.

1. Introduction that provides a quote from which to build the argument. The quote should be used to set up the thesis, a clear claim that will be argued. In this respect, I'm going to suggest/argue (these things never get "proved") that Obama is the right candidate to restore America's integrity in the world.
2. pro-obama point one: leadership
3. pro-obama point two: foreign policy
4. pro obama point three: domestic agenda
5. pro-obama point etc.: whatever else
6. Merits of the opposiing view: either an anti-obama point/paragraph (his shortcomings) or a pro-mcccain point/paragraph
7. Refutation (complete shooting down of the previous point) or rebuttal (evidence that undermines the value of the previous point, which is much more achievable): Why the anti-obama or pro-mccain is NOT significant enough to not vote Obama
8. Conclusion: final appeal to get readers to see why Obama is the right choice.

One could just as easily swap the positions of Obama and McCain in this outline, or plug in a particular issue, or set of issues. It is expected that each of these elements is found in your essay and the assignment will be incomplete without covering all of the expected points.