In Aristotle's Rhetoric, he talks about the topics in two places. In Book I, chapter 2, he mentions the common topics, or koine, which, he says, are four in number: (1) the possible and impossible (2) past fact (3) future fact (4) the lesser and the greater. The idea is that, for every subject, you consider whether or not there are possibilities or impossibilities associated with it. If everything about it is possible, then you have a strong argument for doing it; if there is some barrier that seems impossible to overcome, then the argument for doing it is weak. If the argument includes something that seems inherently impossible, then you have a strong argument for rebuttal. Secondly, if you can prove that something happened in the past, then you can extrapolate from that fact to other likely occurrences. Similarly, if you can show that something will inevitably happen, then you have leverage to argue for or against other things in conjunction with it. For instance, if something is going to happen, then there are opportunities to do something profitable in its wake. Finally, you can compare alternatives and determine which is greater or lesser. Sometimes, you want things that are greater than others; sometimes lesser. The more profitable or advantageous of two options is to be preferred; the lesser evil or damage is to be preferred.
In Book II, Aristotle says arguments can be constructed from twenty-eight topics (many of which seem to be more precise variations on the four common topics:
It's probably not important to try out each of these topics on your subject, or even to figure out what each of them means, but you might try a few, asking yourself questions like:
Try to make questions out of the topics that make the most sense to you and then answer them as you think about your subject. If you do this, you will begin to think of the topics as a guided brainstorming session. Combined with testimony and authoritative commentary, these arguments should help build your case.