- Don't talk down to people
2. Don't shift the burden of proof
Seeing this piece of advice broken is a pet-peeve of mine. Christian have the burden of proof not atheists! Let's review the definition of an atheist. An atheist is a person who lacks a belief in a god or gods. "Lacks" is the key word in the definition. If the definition was slightly changed to: "an atheist is a person who believes that no god or gods exist", a strawman frequently used by theists, then atheists would have the burden of proof. Let's use the analogy of unicorns again with the terms "unicornist" and "aunicornist". A unicornist is someone who believes in unicorns and an aunicornist is someone who lacks a belief in unicorns. Which person has the "burden of proof" or the responsibility to provide evidence for their claim? Obviously the unicornist because they are the ones who hold the positive belief. If you said that the aunicornist had the burden of proof, please leave your reasoning in the comments below so we will be able to discuss the issue. Or, see http://wiki.ironchariots.org/index.php?title=Burden_of_proof for a brief explanation. The person asserting that something is true must provide the necessary evidence. Do not attempt to shift the burden of proof to yourself if you are an atheist. Let the theists dig their own holes because refuting theists claims is much, much easier than trying to prove that no gods exist (that's just a field of land mines).
3. Don't be too respectful of a Christian's religious belief
A person's religious convictions are no more "sacred" than their beliefs on their favorite daytime soap opera. Granted, there is a fine line between being respectful of someone's beliefs and being disrespectful, so let me explain. Always realize that people have the right to believe whatever they want. It's the same principles that allow atheists to hold their lack of belief. In addition, it's their right to not have their beliefs challenged and to stay sheltered from the evidence against their beliefs. This being said, if you both agree (whether explicitly or implicitly) to talk about your religious beliefs or lack thereof, I would prefer that neither side holds back. Christians usually aren't the ones who are guilty of being too respectful of an atheist's position because, supposedly, their duties as a Christian are to defend their faith (1 Peter 3:15) and I think that this is a good thing. Challenging your beliefs in everything, although wholly impractical, is a beneficial practice. Ultimately, I would like to know as many true things as possible, as well as having as few false beliefs as possible. What I don't want to see atheists doing is "going easy" on a Christian just because they are talking about religious beliefs.
4. Don't misrepresent/generalize other atheists' and theists' viewpoints
The only characteristic that all atheists share is a lack of a belief in a god or gods. Although there may be some other aspects that most atheists share, there will never be an "all". Try to avoid sweeping generalizations such as, "atheists believe that abortions should be legal". This may or may not be true for most atheists, but I can guarantee you that all atheists do not feel this way. If your statement begins with "atheists believe..." you should rethink the statement you're about to make. The same rule applies when talking about theists. However, when you get down to the denominational level, there are certain characteristics you can give to people. For example, in addition to a belief in a god or gods, Roman Catholics follow the Pope. Avoid painting theists with a broad brush. Allow the theist to define their version or versions of god or gods to deter from tearing down a strawman. I have heard atheists jumping the gun and arguing against what most Christians believe, only to hear the Christian say, "Well that's not the God I believe in." Don't give them this opportunity.
5. Avoid letting Christians making too many consecutive claims without addressing them
In order to have a productive conversation, you have to figure out where the two of you agree and where you disagree. Don't let a Christian build an argument on premises you find to be false. If you let the Christian lay out their case with premises you find to be false, there is little point in arguing about the Christian's conclusion because neither of you will make real progress. Arguing the points leading up to a conclusion and working through the logical process together (whether both of you agree with each other or not) can only be beneficial. In addition, a common apologist debating tactic during public venues is to make claim after claim after claim so that their opponent has an impossible task in refuting them all. The apologist then claims victory because their opponent couldn't refute their points. If it is possible, pause the Christian's argument as soon as you disagree and start the discussion.
I hope these points have been instructive or helpful at least. If you disagree with these tips or have more to add, please leave me a message in the comments below or e-mail me at firstname.lastname@example.org! Have a great day!