Familiarize Yourself with What Atheism Is and Is Not:
It doesn't make sense to try to discuss atheism, theism, or religion with atheists if you aren't already at least a little familiar with what atheism is. Many churches and apologetics books have misinformed people about how dictionaries and atheists themselves define atheism: it's just the absence of belief in gods, not the positive denial of your god's existence. Some atheists go on to deny some or all gods; others don't. You can't assume you know what any particular atheist does so you'll have to ask. If you at least show familiarity with the arguments, you'll start out on a positive note. What Is Atheism?
Ask Questions, Don't Make Assumptions:
You know what happens when you make assumptions, right? A significant problem which atheists have with theists is how so many make all sorts of assumptions about atheism, atheists, and anyone who isn't religious. Many of the most common myths about atheism and atheists are derived from people making easily dispelled assumptions rather than just asking simple questions. If you ask genuine (not rhetorical) questions and evince an interest in learning, you'll put others in a positive frame of mind and make them much more inclined to discuss things with you. Common Mistakes & Assumptions...
Believe Us When We Say We Don't Believe in Gods and Aren't Religious:
As if making lots of assumptions werent bad enough, some theists presume to know our minds better than we do even though they don't know anything about us except for a few exchanged words online! You can't have a serious conversation with a person if you're going to keep telling them what they "really" think and what they "really" are. That's rude and uncalled for. If an atheist says that they don't believe in any gods and have no religion, you shouldn't try to tell them that they are wrong without very, very good reasons. Atheism Doesn't Involve Worship...
Atheists Aren't Trying to Undermine Liberty or Eat Your Baby:
One sure way to eliminate any chances of a productive conversation with an atheist is to enter it under the assumption that atheists are evil, are conspiring to ban Christianity, or want to harm your family. If that's your attitude, then you should take a second look at why you are trying to have a conversation with someone you regard as so depraved and evil. What is your real goal and what do you expect to get out of this? Atheists get tired of being told that they are enemies of freedom and America, so please don't bother, OK? Atheists Aren't Imposing a Religion on America...
Discuss, Don't Proselytize or Preach Discussion is a Two-Way Street:
There's a difference between a discussion and preaching. A discussion is a two-way street where both contribute and what each person says actually reflects something they have taken from what the other says. In a discussion, you have to listen to what the other is saying and respond directly to it. When a person is preaching, though, they aren't really paying attention to what the other says. None of their statements reflect their having noticed or taken anything from others. If you want to have a discussion with an atheist, great, but please don't use the pretense of a discussion as a platform to practice preaching.
Is it Possible That You Could Be Wrong? If Not, What Are You Doing?:
Ask yourself if it's possible, at least in theory, that you could be mistaken about things you believe (regarding theism and religion). If so, then a discussion or debate with an atheist has the possibility of providing you with something to learn and think about. If not, then what is the point of having a discussion with an atheist? Is it just something you are doing to preach and hopefully convert them? If so, see above. Please take stock of your motives and goals before proceeding because you might find that you aren't going into this with the best of intentions.
Familiarize Yourself with Common Errors in Reasoning & Logical Fallacies:
It would be nice if schools in America merely did a poor job at educating students in logic and arguments, because most do no job at all. Few people even know what a logical fallacy is, much less how to identify one in an argument. Atheists make plenty of mistakes in this, too, but when theists offer arguments in defense of theism to atheists it's common to see the same mistakes over and over. If you're going to talk to or debate atheists, please become familiar with common mistakes and fallacies which people make: you'll be able to avoid them and you'll notice when others commit them. Logical Fallacies...
Familiarize Yourself with Common Arguments & Common Refutations:
Atheists often hear the exact same arguments over and over from one theist after another. This isn't surprising because there are a limited number of arguments defending the existence of gods, but the problem lies in presenting the simplest forms of the same arguments. There is rarely any evidence that the theist realizes either that there are more sophisticated versions or that there are easy refutations of what the theist is offering. Providing the same, obvious rebuttals to the same, superficial arguments gets annoying, especially when more interesting options exist. Common Arguments for God...
Just Because the Bible Says It, Doesn't Mean that Settles It For Us:
Many Christians treat the Bible as the first, last, and ultimate authority for everything in their lives. It records instructions from their god and, of course, their god isn't to be disobeyed. Atheists don't believe in the Christians' god, obviously, and therefore also don't believe that the Bible has any special political, moral, social, or religious authority. Christians don't always realize this and as a result sometimes quote the Bible in discussions with atheists as through these passages should settle any disagreements. That just won't work, though, so please try to keep this in mind.
Don't Pray for Us, Or At Least Don't Announce that You're Praying for Us:
It happens far too often that a theist will tell an atheist "I'll pray for you." Atheists obviously don't believe in the power of prayer, but even the theist who does can't believe that prayer will be more effective for having announced it to the atheist. So what's the purpose? Some say that it's to express well-wishes, but in that context people say that they'll pray for someone when the person is sick or having trouble. One way or another, the theist appears to be expressing superiority over atheists in a passive-aggressive manner that atheists often interpret as rude, arrogant, and condescending.