Maybe it's something hanging over from when I evangelized the Christian gospel. I feel like I want to grab someone by the shoulders, shake them, and say, "Listen, have you heard this? Isn't this amazing? Don't you feel like you should do something?" The problem is that there's just so much to address; our world is in dangerously short supply of rational thinkers, especially in positions of authority, and credulity is practically being bred into us. Unreasoning, unskeptical thinking is encouraged, even promoted as a value under the guise of faith – and thus expected to receive some inherent level of respect from all and sundry.
The major problem with the idea of "atheist evangelism" is that atheism really isn't something that can be promoted, per se. It's not a product; it doesn't offer any benefits; it's not a quick and dirty solution to difficult problems. These are the sorts of things people tend to be looking for. Atheism is typically defined as either a lack of belief in gods or rejection of claims made about gods. That's basically it; it's a conclusion drawn about a single subject. Pure atheism doesn't really give us much to work with. There's also the problem that the fact that someone is an atheist doesn't necessarily mean that they've got their head on straight. Atheists aren't always rational, any more than religious people are. Rational thought goes well with atheism, but atheism certainly doesn't require it. (Just look at the Raelians, for example...)
So what should atheists evangelize, if anything? I'd put my money on critical thinking, skepticism, reason, the scientific method, and open-mindedness. From what I've seen, these things tend to lead people to become atheists more than anything else, especially when they're applied to concepts that believers take for granted. Properly applied, these tools can help us find the best solutions for just about any problems we face. If, in the process of using them, a believer becomes an atheist, so be it; in my mind, it's more important just to get them using the tools in the first place. Better to be religious and a critical thinker than an atheist and gullible.
I don't think atheists should evangelize simple doubt or disbelief in claims made by religion. Any fool can doubt religious beliefs; it takes reasoning and critical thinking to figure out why something should be doubted. Simply going around telling people that religious claims probably aren't true isn't good enough. For one thing, it's very difficult to reason people out of positions that they didn't arrive at through reason; for another, it doesn't really address the core of the problem, which is a lack of critical thinking. Let's say you manage to dissuade a devout believer of all their supernatural beliefs. Does this really accomplish anything? Instilling disbelief isn't the same as planting the seeds of analytical thinking and skepticism about faith-based claims. You can believe a lot of true things for the wrong reasons; you can also disbelieve a lot of false things for the wrong reasons as well.
The ability to critically analyze claims based on their evidential merits is one of the central strengths of freethought. By employing the contents of a basic skeptical toolbox – a better knowledge of logic and fallacies, an understanding of the scientific method, and other parts of Carl Sagan's "baloney detection kit" – we're able to figure out whether or not something is true, typically with a better likelihood of being right than if we had just gone with our gut or accepted what we were told. I believe that, if we help people build their own toolboxes, we'll stand a better chance of turning the tide in reason's favor.
Now that we've got an idea of what to promote, the big question is how we promote it. Faith and unscientific credulity are strong forces to contend with, and it's easy for a believer to block out any skepticism about their sacred cows if the skeptics come about the discussion in the wrong way. Popular culture also has a tendency to promote bad science, through TV shows that promote pseudoscience, news reports that give an undue amount of respect to fringe claims (in the name of "balance"), celebrity endorsements of new-age mysticism, and so on. The "woo" has a long head start in this race, but there are a few ways we can fight back.
First, get vocal. If you see something you think is fishy (in the news, on a TV show, etc.), do a little investigation. If you can, find out what the scientific consensus on the subject is. Write a letter to the editor in response to sketchy journalism, or pen an opinion piece critiquing the scientific or logical flaws in the rhetoric of pseudoscientists. If you think someone is using good science to promote bad ideas or bad politics, make your voice heard. If you feel it's necessary, contact your congressional representatives and speak your mind.
Second, get excited. Part of what's so fantastic about science is that there's so much awe-inspiring mystery in the natural world alone that we don't really need all the mystical supernatural stuff. Share your love of science and your fascination with science news with your friends and family. Let them know why it's important to you and why you're so hyped up about it. Promote the idea that science is open to everybody. Unlike what we see on some TV shows and in movies, science isn't some arcane, mystical process that is inaccessible to anyone who doesn't have an inborn special talent for it. Anyone can be a scientist, as long as they keep asking questions. If you've got kids, encourage their curiosity; if they keep asking "why, why, why," don't just give up when you don't know the answer – look for the answers with them, and help them learn how to find things out for themselves (rather than just accept it "because we said so"). Lighting the spark of investigative curiosity and critical thinking is essential for helping make the next generation more freethinking than the current one.
Third, get invested in the future. When it comes to science and critical thinking, much of the American educational system is in dire need of an overhaul. Kids are taught to memorize formulas and to try to get predetermined results for their science experiments. Find out what can be done locally to influence the science curriculum. Demand that kids get the education they deserve. For example, you could suggest that, rather than follow a strict plan for doing an experiment, the kids are told to design their own experiments and justify their methods by explaining why the science supports their ideas. Anything we can do to promote "teaching to understand" rather than "teaching to memorize" is worth pursuing.
Fourth, get suggestive (rather than combative). There's no better way to push away a believer in any irrational claim than to just tell them that they're wrong. Instead, get them to question their presuppositions in a way that makes it seem like it was their idea in the first place. If you hear someone talking about a pseudoscientific belief, ask loaded questions that are intended to guide them into critically examining their ideas. For example, if you're talking to someone who suddenly brings up astrology and how their horoscope said that such-and-such a thing would happen today, ask them if it doesn't sound like a pretty safe guess, or if it makes sense to think that it would happen to everyone born during the same period of time (and nobody else). In other words, rather than throwing a brick wall up in front of them, quietly slip in a roadblock that makes them pause and reflect upon what it is they've accepted as true. Passively planting seeds of doubt this way is a sort of kinder, gentler skepticism that usually doesn't come of as dismissive or disrespectful.
Finally, get skeptical! Skeptics are a major part of our front line in the battle against nonsense, no matter where it comes from. The more positive we are as skeptics, the more likely other people will be to pick it up as well. Get familiar with logical fallacies, the scientific method, and the flaws in human judgment (faulty memories, sensory misinterpretation, cognitive biases, etc). Familiarize yourself with common rhetorical techniques that the woo crowd will use to trick people into credulity, and try to figure out their potential ulterior motives. Most importantly, don't jump to conclusions. Just because you're a skeptic and a claim sounds unbelievable doesn't mean you're necessarily right; you've still got some hard work to do to find out what's most likely to be true. After all, skepticism of a claim is just the beginning of the investigation, not the conclusion. Besides, human beings are often self-deceived about their abilities or the depth and validity of their understanding of a subject (something called the Dunning-Kruger effect).
I'm sure some people will disagree with my analysis. They're welcome to do so; after all, what kind of freethinker would I be if I demanded that everyone agree with me? Regardless, I hope that at least something I've said here will inspire all freethinkers to evangelize what really matters: science, reason, critical thinking, and skepticism. Given time, I'm sure that these will do more to fight against the old dogmas than anything else.
Science may be hard to understand. It may challenge cherished beliefs. When its products are placed at the disposal of politicians or industrialists, it may lead to weapons of mass destruction and grave threats to the environment. But one thing you have to say about it: It delivers the goods.
-- Carl Sagan, from The Demon-Haunted World: Science as a Candle in the Dark