A friend just asked me how I would respond to the question "Does God Exist." Here's my spur of the moment response:
The short answer is yes, God exists. I assume you are curious as to my reasoning.
The only way that I will ever debate this is roughly as follows (and remember--pick your audience. Whom are you talking to--the guy across from you? The crowd? Then tailor your argument to their needs--this one is made for the audience):
1). Make circular argument: "God exists because He says in His Word that He exists."
2). Wait for screaming to start: "Petitio Principii!! Petitio Principii!! Circular reasoning! You're an idiot!"
3). Look bemused (give it a second, wait for the volume to die down).
4). Affirm that it is circular reasoning, and state that God cannot be rationally proved apart from circular reasoning, and you're not interested in trying--He commands us to accept Him on faith, and you're going to. After all, He Is God. Then,
5). Comment that you also believe in God because of the impossibility of the contrary--without God, it is impossible to prove anything.
6). Wait for the rabid denial to die down (always look amused, never, ever, ever be threatened or shrill--the moment you argue, you've lost. Don't argue, simply illustrate--you are the long-suffering teacher, and the atheist is your bitter, angry, rebellious and slightly dense pupil. God is in control, so act like you actually believe it, as your demeanor does more to the crowd than your logic ever will). When the denial has died down, ask them
7). Do you believe in reason? Get them to say yes--if they aren't an idiot, they will.
8). Then say, "Can you give me a reason to believe in reason? Oh, actually wait--can you give me a reason without using reason? Don't want you to be guilty of petitio principii (peh-tit-eey-oh prin-kip-eey-eey: this is an obvious humor and ethos card to drop--1, it shows that yes, you do know this logic stuff, and 2, you find this whole thing kind of funny. Grin at some friendly face in the audience, chuckle a bit).
9). Then, deal lightly with their response (some variation of "Nuh-uh! Is not circular reasoning!) by 1), patiently making the point over as if they just aren't seeing it (which is usually true), or 2), sidestep and hit this point from as many angles as you can--show how reason has to be assumed for them to prove anything, then comment that you believe in reason because it reflects the Nature and Character of God--why do they? Because it works? Well, they might want to practice using it a bit more, as they still don't seem to be able to see where they were just blithely assuming enormous leaps of logic (say this in an almost concerned fashion, make sure to sound sincere, or you sound like an ass).
That's about it. But I only ever debate to affect an audience, as debates never change the minds of those debating. Those, you invite over for dinner, dessert and a movie, and you demonstrate the love and life of Christ to them. After all, they are depressed, bitter, lonely and very, very scared--to them, be a haven and a blessing. Be courteous, be loving, and always be two steps ahead--God is Wisdom, we have no excuse for not using it.