Atheist here, although I debate theology from the position of an agnostic. Lots of experience debating fundamentalist Christians IRL and in chatrooms. Here’s what I find works.
First and foremost, know whom you’re debating. Before things get hot and heavy, take a moment to find out where they’re coming from. The operative word here is “why” as in “Why are they a fundamentalist?” The answer might surprise you. I learned this lesson the hard way. I was debating with a fundy in a chatroom, and things were getting pretty intense. Tempers flared on both sides, the debate turned personal, and finally I snarkily asked why she was so fired up about Jesus.
It turned out that she wanted to follow Jesus as best she could, because she believed her five year old daughter was waiting for her in heaven.
That conversation has stuck with me a long time, and five years later, I wish I could take some of what I said there back.
Secondly, on that point, don’t get frustrated, don’t raise your voice, and never show anger or belittle them. Remember that you are probably not the first person they’ve dialogued with, and unless they are from deep within the Bible Belt and have never chatted on the Internet, they’re used to being ridiculed, argued with, and marginalized. Whether they deserve this or not is a matter of debate, but doing any of this will certainly shut down communication quickly, and while you might continue arguing, you will not be communicating or dialoguing. Indeed, by keeping your cool through the debate, you’ll likely surprise them pleasantly.
Thirdly, keep your composure and act kindly and politely no matter what they say to you. As I’ve said above, these guys are used to put-downs, and they might very well act like pricks out of defensiveness. If you want to dialogue with fundies of any stripe, you’ll have to learn to accept that as part of the territory. More often than not, the hardest, most backward fundies will lighten up and start speaking civilly once they realize you’re not out to bust their balls for the hell of it. Occasionally one or two might even apologize for their previous behavior (But don’t count on it.).
Hope that helps. 