I care a lot about what religious people think. In fact, if you're going to try and get religious people to give up their views, it's pretty important to understand how many of them think. So this post won't be about getting people on your side or encouraging discussion (for how to find secularists and atheists and similar people, I recommend watching this little speech by Jen McCreight). I'm going to look at the religious, and the sorts of thoughts and feelings you can expect to find going on underneath their skin.
But first, a little about myself. I was a devout Catholic up until a few months ago (I know, right!?). This meant I engaged in apologetics, mostly with myself and other Christians, and I went to mass every Sunday and on the important Holy Days. Hell, I even went to confession once in the past four years, and what a tearful experience that was (though the Priest ended up weeping more than I did, more than I'm capable of, I suspect). Oh, what a grand old time that was. It's amazing what you'll do and say when you're engaged with holy fervor and zeal. So, following that confession, my year and a half journey to atheism probably seems pretty quick. Well, it wasn't, and it isn't an easy sort of thing to go through either. Most of the faithful are aware of the things that move us away from theistic beliefs, and they go through hoops and loops like you wouldn't believe to keep their faith firm (it's all bullocks too, and not firm bullocks, which I think we'd all prefer). So what I'm going to do is tell you a little about how to convert people like me.
You cannot convert people like I was. It's impossible. Anyone with a modicum of true faith will resist giving up their beliefs like your keys resist being discovered. Every impulse in their brain (or nearly every one of them) charges the mind with zeal and fervor, literally blinding them to rational arguments. This isn't total blindness, it's just the sort of thing that leads to a very narrow world view with certain axioms assumed to be true.
The first axiom you cannot change is that "God Exists." This axiom is literally unassailable. You will not convince a theist that his or her beliefs are wrong by saying "god doesn't exist," or pointing out contradictions and problems with this view. Hume argued that if things need a creator, then god needs a creator. If things don't need a creator, then we don't need god. This argument falls flat against faith because the religious will point out their belief in god stipulates that god is omnipotent and eternal, and does not require a creator, though the universe does. So any argument that god is not a necessary condition for the universe will fail. I say this only to illustrate a point: the religious person's arguments are observational and not conditional (they postulate that god exists and created the universe rather than the universe needs a creator). This is circular, but most axioms are, and pointing out the circuity of this beliefs won't get you anywhere.
Instead, insist that god is a superstition and point out the lack of evidence for belief in god (note that the universe doesn't need a god to exist from a logical standpoint, but don't insist on this as disproof of god - instead, it's a more elegant hypothesis).
So we've stopped trying to convince people that god doesn't exist. Don't worry, we're not giving up the gun. We don't want to lecture or instruct people in the belief that god doesn't exist. For one thing, as Dawkins points out about religious upbringing, there is something inherently abusive in such orthodoxy. As atheists and secularists (and, in my case, an instrumentalist and naturalist) it is much better to show the believer all the things that seem to contradict the necessity of god. They will do the rest of the work themselves.
This leads to apologetics. It is our duty to help the religious along the path to reason and truth. Feel free to disagree, but I see religion as dangerous cognitively and socially, and the less influential it is in general, the freer our societies will be of things that belong in the privacy of home or places of worship. How can we do this? Be friendly, engaging, and debate the opponent. Never stop insisting that god isn't real or isn't a reasonable belief (I think saying god isn't reasonable to believe in works better than saying god doesn't exist). The religious person will not debate the merits of those points directly (typically), instead he or she will engage in apologetics, to try and defend god from the perspective of their faith.
Brief Aside: Apologetics are unbelievably stupid and silly. Many of you will say, "god doesn't exist," and find yourself debating whether god is good, or good is consistent, or whatever. This is a debate of theology versus rationalism. You point out rational problems, they point out why a problem isn't a problem. I can't begin to count the number of times I have proposed that god doesn't exist and there is no evidence of it, and found myself discussing some biblical trivia (or, when I was devout, unconsciously guiding the debate to apologetics and justifications of god, rather than the discussion of god's existence).
But the good news is you CAN win apologetics debates without too much trouble. When you win a debate on apologetics, you aren't winning a final, lasting victory. Instead, you're goal should be casting doubt on some tenant of the faith.
As an example, say someone believes in original sin. Original Sin isn't mentioned anywhere in genesis, and the rest of the bible only really alludes to it. Some poor translations substitute original sin for different terms or ideas, and historical jews didn't believe in original sin. Moreover, St. Paul once wrote that nothing is sinful unless the sinner acts maliciously against god. So, arguably, people are born sinless and there is no such thing as sin, unless maliciously aimed against god (having an incidental orgy is fine, just make sure no married people participate and that you have the fee to pay for any female virgins who get deflowered!).
This is one interpretation of a few biblical passages. There are many possible readings, and the devout will try and debunk the rather unfamiliar notion that orgies are fine and people can't sin. You can also debate free will and sin similarly (it comes up frequently). The inconsistencies are glaring and the faithful will come up with incredibly clever apologetics to deal with it (the lack of sin is one such solution, another I've heard is that god lets us sin for his own glory when he forgives us, though that one implies that god created us knowing we would sin, so how can we sin if it was inevitable and glorifies god. It would make sense to sin more frequently, so as to glorify god more often, etc, etc). The more you confront the theist with holes and problems in their beliefs, the greater and more general their apologetics gradually become. You can literally take a christian fundamentalist (a thinking one who just wants to be a good christian) and guide them from fundamentalist to anglican (you know, barely christian - no offense to you anglicans ;p) given enough time and exposure. It's a long and difficult process. When contradiction arises, willful ignorance or accommodation are the only outcomes. If accommodation is their response, then you need only patiently and slowly point out contradictions and problems until the faithful person comes to the sudden realization that they don't need god and god probably doesn't exist.
Just remember, some people will resist conversion no matter what, and for most of us who were truly faithful, giving up our beliefs is a difficult and painful process. No faithful christian will toss aside their faith at the drop of a dime.