How does the system know what particular category a question should be in?

Not sure exactly what you mean by "category," but your question is organized by the topics you file it under, in your case "how to","logic" and "category". Yahoo Answers is a little less flexible, with every question just filed under a single category. Either way, there is no magic algorithm that decides where the question goes, it's just part of the data entered by the asker.

Fluther does have an algorithm that decides who to guide the question to, but I don't believe that's what you're asking about. Does that clear things up?

that's exactly what I am asking about.Thanks Ben.

Also (depending how quickly you type and whether you look at your fingers), you'll see suggestions appear as you type in your topics.