One thing I forgot to mention is what to do when you're confronted by someone who is using a red herring argument, or some other logical fallacy (such as ad hominem or straw man). One thing you definitely should not say is, "Don't you know that your response to my argument is irrelevant?!?" I know this is tempting, especially if you are in a heated debate with someone.
Instead, you should respond with patience and grace, yet not giving in to the other side. (Kind of like turning the other cheek). Say something like, "I appreciate (or even agree with) your argument, however I would like to point out that it does not directly address my points." And then politely explain why, and then say something like, "I am still waiting for an answer to my argument."