First, Be Real.
You have the same life challenges as anyone else whether believer or unbeliever. That gives us a lot of common ground for conversation. Capitalize on this. Be curious about the lives of those you come into contact. Ask questions about their life, family, work, education, and cultural background. People love to feel special, and anyone who will ask about them will likely be far more transparent than you expect them to.

Also, you should be transparent about your life and the issues you face. Just because you're a believer doesn't mean you don't have challenges. They may be, after all, the same challenges a friend who is not a believer is encountering. God does not solve all our problems but walks with us through them. We all live by faith. Share your challenges and invite them to share theirs. And then gently and carefully weave God into your story, and watch and listen to how they respond. Belief in Christ is central to who you are, so don't be ashamed to proud of what God has done in an through you - but take slow steps.

Second, Ask Non-threatening Spiritual Questions.
Think about these sorts of questions:

1. Tell me about your spiritual journey? Allow them to go anywhere they desire with this rather broad "faith" question. Listen and where appropriate share your story experience as is both aligns and diverts from their experiences.
2. How are you handling those challenges? When someone is sharing deep pain or tough situations, this is helpful to learn what they do and how they find help. We know God alone heals, so this might be a good point of entry for guiding someone to a God who saves.
3. Do you have a spiritual practice that helps you through these times? Again, a wide-open question which assumes nothing and is non-threatening.
4. Are you a person of faith? You should not assume your understanding of the word "faith." but this question leaves the word "faith" open for their interpretation. It merely invites a conversation.

Third, Be Ready And Willing To Tell Your Story.
While our circumstances are different most of us can relate to the stories others tell us. Be ready to tell yours. Share the hard things, maybe how you handled a situation in the past and how your faith fits into your story.

And remember to empathize. People are hungry for someone who will say to them, "I get it, I'm sorry you are walking through this situation." Or if it is good news, "I'm excited for you." You don't need to push Jesus on them, just tell your story and see where the conversation goes. Your conversation with them may be a defining one, or it may be a touchpoint God has for this individual along the way and one they may remember later and consider.

Be you, be real, be inquisitive and be ready to tell your story.