Hi everyone, I'm a long-time-mostly-lurker here, and this thread struck a particular chord with me today because I have been reading and thinking about witnessing. I've even started to venture out on my own and telling my best friend (an Orthodox Jew) about Christianity. Though some of the stuff I'll say here is probably a repetition, I figured I'd add my two cents, because I grew up, went to school/university/grad school, and have essentially always been surrounded by atheists. In fact the first step I took toward Christianity was a rejection of the atheist "logic" I was surrounded by. I'm not an expert witnesser by any means, I don't know all the theory and everything behind it, but I do know atheists...
Like many people here have said, arguments about hell and sin and the need for Christ for salvation aren't the way to go in the first conversation, and you can't expect to get a conversion via street witnessing, though there are still reasons to do it. For instance when I was in college, the students out there witnessing on the streets were by far the most accepting people I talked to there. If you can be that, you'll at least get the attention of people who may feel like misfits or outcasts. Again, though, that isn't done by talk of hell or sin.
Talking to atheists, though, all you can really do is plant a seed, and it may take years to fully develop, but if you can get them to just change their perceptions of various stereotypes you have been successful. In atheist eyes, Christians are either bullies who tell people they have to think/feel/act exactly as they do, or they've been forced to submit to the bullies because they're weak and believe in faulty logic and unprovable stories (whether Biblical or of "miracles"). The core of their belief system (for lack of a better word) is that religion, itself, doesn't give anybody benefit in their lives. When you know what you're dealing with, though, there are ways around it.
Because there *are* tangible ways that a belief in God benefits us in this lifetime - no thoughts of Heaven or fear of hell necessary. The fact is that even if I did just go into the ground and cease to exist when I died, I would still count myself blessed for having the presence of God in the time I was alive. That I can know He's with me when I'm loneliest, and that He loves me when it feels that no one else does, and that God's will provides some order to the universe is a powerful thing. Prayer to God is a comfort to the person praying as much as it is a duty; it's a way of getting hardships and worries off your chest and releasing them to Someone who can actually do something about them. It's meditation on steroids.
You're not going to convert them using that line of rhetoric, but they'll remember their conversation with you because it was different from any conversation they've ever had with a Christian, and hopefully when they face the next hardship in their lives - and EVERYBODY faces hardship - they'll see that praying to God is a whole lot more comforting than not praying to Him.
The other thing I'd say about witnessing to atheists is that it's beneficial to avoid the "gotcha" questions. "Why do bad things happen to good people" is an easy and necessary one to answer, and a good answer to that can get them thinking. When people ask you if gays go to hell, though, you just divert the question. God loves all people, though all are sinners and he hates all sin (acting on homosexual impulses is a sin, but heterosexual people sin, too), it's not up to you to judge them, all you are trying to do is help people understand God.
Essentially I'd say that spreading the Word to atheists is most effectively done through a discussion of God's love and nothing else at first, and that pure love is actually one of my favorite ways that the teachings of Christianity differ from those of other religions. Jesus loved sinners, prostitutes, the lowest of the low by society's standards. They've heard the basics (or at least horrible interpretations of the basics) a thousand times; tell them something new and you'll at least get them thinking about how to argue with you.
