|Julian the Apostate|
1. Be open about it. This might be easier said than done depending on your family situation and where you live. If you think that you can still maintain your important relationships (not to mention your career) with this revelation, then let people know where you stand. I'm not saying that you need to confront people and get in debates, but don't let people assume that you're something that you're not. I wrote before about how atheists can learn from the struggle for equality that gay people have faced. Many people have come to accept gays and support their rights simply by realizing how many of them are around them and learning that they're really not all that different from them. When more believers realize that apostates don't become cat-sacrificing meth-heads upon deconversion, then we'll start to become less scary to them.
2. Be prepared to hear points as though you've never even considered them, even though you've spent much time pondering and ultimately rejecting them. If you follow my first piece of advice, then you're probably going to find this to be one of the most frustrating things. Did you spend a long time thinking about the various arguments for the existence of God only to find them wanting? Did you even use to say some of them yourself? Don't expect any of that to matter, as you'll hear everything from the ridiculous "Why are there still monkeys?" to the more thoughtful (but ultimately flawed) "The universe must have a case that exists outside of itself, and the best explanation for that cause is God". Not only will you hear all of these arguments, but believers will say them as though you've never given them any thought - even when you demonstrate that you have. They'll likely then accuse you of being close-minded and/or biased (even though you have already demonstrated that you can change your mind and overcome a bias).
3. It won't matter that you used to believe. This certainly seems to be the case with Christians in particular, but I imagine it's probably true for other faiths as well. Once you tell somebody that you don't believe, they assume that the problem is that you somehow don't know the theology. The problem won't be that you've found some flaw in the system. Clearly, it's that you don't know anything about it. Much like in my last point, even when you explain that you were a firm believer, many theists have a hard time accepting that one can sincerely believe and then change his or her mind. You might even find this happening with people you've known your whole lives and prayed next to in church. Prepare for frustration.
4. They will assume things about you. Without even listening to your objections, many believers will immediately start formulating a narrative in their heads about why you feel the way you do. Obviously, you're angry at God. Or, you had a bad experience. Probably the most helpful thing you can do is, instead of debate, simply explain why you don't believe (rather than telling them why they shouldn't believe).
5. They're not interested in what you've found out. For some nonbelievers, coming away from faith feels like stepping out of a prison where you had the key all along. You step outside the bars, look back, and wonder how the hell you could have stayed in there for so long. And then you see your friends and family and you want to yell at them: "Hey! Look in your hands! You have the key! It's obvious!" Unfortunately, instead of them thanking you, they'll insist that they're not in a prison and won't even look to see what's in their hand. The truth is, many of them are perfectly happy in there. Their families and friends are there. They like the music. They like the camaraderie. For some of them, it's actually pretty comfortable and they have a lot of space to move around and the guards are pretty nice to them.
I realize that any believers out there are probably feeling a bit insulted with this analogy. Please realize that I'm trying to address nonbelievers, and whether we're right or wrong, this is how it feels. Many of us want to help others get away from faith, but the reaction on the part of many is to completely reject what we have to say rather than even consider that we might be on to something.
6. If you debate, stick with conversations about evidence. I think that I've learned this one the hard way. I've gotten into long debates about issues like how the Bible endorses slavery, and ultimately it's just frustrating and pointless. Apologists will excuse anything, no matter how horrific, that's in The Bible. (If I had a nickel for every time I heard the intellectually and morally bankrupt "Slavery was different back then/It was more like indentured servitude!" argument, I'd have a hell of a lot of nickels.) Ultimately though, these kinds of discussions are pointless. Let's say that The Bible clearly stated that owning human beings was wrong. Would that suddenly make the Christian God real? No. You'll find better morals in the average Superman comic, but that doesn't make Superman any more real than Jesus.
Stick with discussing what you both consider to be evidence, and then determine whether such evidence exists. Don't hold your breath thinking that they'll give you something, but be open to hearing about it.
7. Remember that they're not stupid. Don't get all tribalistic about this and assume that those on your side are somehow smarter than the opposition. There are plenty of bad reasons to become a nonbeliever, and a lot of atheists and agnostics aren't very thoughtful about their unbelief.
8. Beware the condescending nonbeliever. If you're the kind of person who likes to debate this stuff, don't be shocked when some of your fellow nonbelievers think that you're somehow doing the equivalent of what the Westboro Baptist Church does. It's funny, because even though I'm very public in my nonbelief, I've found myself making friends with a lot of Christians. It's weird, because they send me friend requests. I even get a few +1's on Google Plus from believers on some of the blog entries I've written.
However, talking to some atheists and agnostics, you're creating the crime of all crimes by critiquing an idea. They act like believers are little children holding on to their teddy bears, and you're trying to tear them away from their beloved toy. Are there some atheists who are obnoxious and insulting? Sure. But even in that case, you'll find that most believers can handle it just fine. They're not as fragile as you think.
The ironic thing about this is that in an effort to be more open and tolerant, these kinds of nonbelievers wind up being the most insulting of all.