Check Your Ego at the Door — You're Not More Rational For Being an Atheist:
Many theists act like simply being an atheist is a sign that they are more rational, more logical, and perhaps even more intelligent than theists. None of this is true. An atheist who has spent a lot of time studying logic and philosophy may be more rational than a theist who has never gone beyond their Bible, but even so it's a mistake to simply assume that this is true of anyone you're talking to. That attitude will do more to push people away than to make your position more appealing.
Ask Them to Define Their Terms, Especially What Their God is and Is Not:
Most theists seem to be more accustomed to talking about their religion with other believers who share the same assumptions as they have. This means they aren't used to defining or explaining their key concepts, especially the nature of what their god is. That, however, is precisely what they need to do with nonbelievers who don't share all of their assumptions. You can't have a meaningful and productive discussion if the two of you define key terms differently. You cannot evaluate their arguments and claims unless you know exactly what they mean by "god," so you have to start there.
Ask Questions, Avoid Making Assumptions:
You may have debated a hundred different theists, but you should avoid assuming that the next is like all the others in terms of what they believe, what they think their god is like, what they know, etc. Any arguments you have against their position must be based on what their position actually is, not simply on what you assume it is. Even if it's a fair assumption, the entire structure of your argument will collapse if they reject one premise. There is enough variety, even within Christianity, that you can never be sure. You can avoid this by asking them to explain what they believe and what they mean.
Ask Them to Support Their Claims When they State their Claims:
Many atheists constantly ask for proof, but proof isn't always appropriate. Not every claim has to be proven to be reasonable, fair, or justified. What's necessary is some level of support: some claims require more support, others require less. Theists who make claims of any sort should be asked to support those claims; if they don't specifically claim something, they shouldn't be expected to support anything. If they make any claim which can only be adequately supported by proof, for example something based on numbers, then they should be asked to provide that proof.
Be Prepared to Support All of Your Claims:
Religious theists are frequently criticized for not adequately supporting many of their claims. Precisely because these criticisms are often justified, atheists who debate theists should make a point of not doing the same thing. If you are going to make any specific claims, you should be prepared to back them up by whatever support is most appropriate. If you can't, then you shouldn't have made the claim in the first place; it would be best to admit that you can't support the claim, take a couple of steps back and start again from a stronger foundation.
Familiarize Yourself with Common Errors in Reasoning & Logical Fallacies:
One of the most significant problems in all arguments, no matter what the subject, is that most people are so unfamiliar with the basics of what a sound logical argument is. People don't know how to construct one and they don't know how to avoid the most common errors in reasoning. People don't even know what logical fallacies are, much less how to identify them. You need to become familiar with these errors and fallacies — first in order to avoid committing these fallacies yourself and second to be able to deconstruct fallacious arguments offered by others. Logical Fallacies...
Try to Be Patient When You Hear the Same Argument for the Millionth Time:
Chances are, you'll hear the same arguments over and over and over. Just because you've heard this argument for what seems like a million times, and phrased in almost the exact same way, doesn't mean that the theist in question has made it a million times. This may be the first time, in fact, and such debates might be new to them. It will be difficult to remain patient in such a situation, but you need to try. If you don't want to spend a lot of time on the same things again, provide links to basic responses and refutations of the argument and see what they do.
Try to Find and Build Upon Points of Agreement:
Debates can be difficult and hostile forms of interaction. Too often people leave them feeling worse than when they started; people trying to make themselves feel better during a debate is a frequent source of mistakes and poor reasoning. It may not be possible to avoid this completely, but a good way to try is to try to diffuse hard feelings early on by searching for points of agreement in the midst of disagreement. If you can at least find things which you both agree on and share in common, it may cause the disagreements to lead to fewer hard feelings and hostility.
Don't be Distracted by Superficial Issues — Find the Fundamental Disagreements:
No matter what the subject, many debates and arguments occur over what amount to superficial or secondary issues. It may seem hard to believe, but it's true — people argue over the products of much more fundamental disagreements than over those fundamental disagreements themselves. Atheists and theists argue over the validity of religious experiences, for example, instead of discussing their different ways of forming beliefs and evaluating evidence. These discussions may be more productive if people focus on these more fundamental matters first rather than last (or even not at all).
Avoid Open-Ended, Directionless Debates That Go Nowhere:
Too often, debates between atheists and theists just drag on and on, going no where and producing nothing. This just creates emotional and psychological burdens on the participants — and for no good reason. Why would you want to do this to yourself? It's important to learn to recognize the signs of such debates and how to gracefully, not to mention quickly, exit them if you find yourself caught up in one. It may be helpful to make some decisions early on about what you want to get out of a discussion and what you want to accomplish, then it will be easier to realize when it's not going to work out.