Q: How do I answer tough questions from non-believers such as, "How do you know God exists?" or what do I say when they say, "I don't believe you, he's never done anything for me." What do I say or do when all I seem to get is more challenging questions beyond what I can answer?
A: I think it's great that you're getting into these discussions. That means that you're investing in people's lives outside the "huddle" and you're approachable. Keep it up. And don't get too flustered by not being able to answer every question or hitting dead ends. People who ask tough questions are usually a lot closer than those who are apathetic and disinterested. Even the most hardened skeptics, if they're engaging you in these types of conversations, are usually at least somewhat open to God.
Sounds like you're already sharing your own faith story. It's hard to argue with your personal experience and that's one of the most powerful ways to share the good news. It doesn't prove anything, but it speaks loudly to most people's lives, especially if you touch on something that connects with their lives.
If your friends like reading, there are a lot of books that might be good to recommend. If they're looking for hard evidence, The Case for Christ and The Case for Creation by Lee Strobel are good bets. If they have hard questions about more personal issues, The Case for Faith by Lee Strobel is very good. Two books that might connect with some folks include Simply Christian by Tom Wright and The Unknown God by Alister McGrath. Other authors to read and recommend include Ravi Zacharias and Charles Colson. Rob Bell might also connect and Letters from a Skeptic by Greg Boyd's a modern classic.
Keep learning and growing. There's no shame in saying, "I don't know, but I'll try to find out." It will keep your faith keep growing and sharp.