How to Reach Out to People Today with Good News

What follows are a few recommended steps to telling our story differently [evangelizing] in a society that has become mistrustful of Christians and all we have to offer. I would add, be willing to use a little well timed humor to make a point.

1. Apologize for past hurts: It never hurts to say "I’m sorry for the way Christians have misrepresented Christ. I’m admitting the church fell short in many ways representing Jesus as written about in the Bible. As we aren’t perfect, we simply can’t. We fallible Christians want you to know we are aware of our discrepancies. I'm sorry if some of our members have hurt you." At that point, the person engaged can see a person humble enough to say "we aren’t perfect, we’re all broken. We don’t get it right every time and we know it." There is no point in saying anything arrogant about having arrived ... we haven’t. We're on a journey. This is a posture that is far different from typical evangelism.
2. Move from talking to listening: “How are you?” “Who are you?” Think of evangelism as at least half listening, not all talking. Also listen to the person’s story. This is the relational, postmodern thing to do. You can even ask (if you're brave enough), “What would you say to Christians if you had the opportunity?” But if you do, be still and listen.
3. Moving from strength to weakness: Let people know you understand that you are ordinary and imperfect, just like everybody else.” Be willing to let people know: "I’m still journeying and will say I don’t know to your questions when I don’t." Be honest about what we know and what we don’t. None of us have to make things up to be okay. Affirm questions and discuss them. Explore them together and learn something together. This is an attitude and posture different from others.
4. Shift from speaking of beliefs to spirituality: “I want to talk about God, not religion.” Emphasize God and spirituality. Spirituality is our relationship with God. It is how God speaks with us. People have largely rejected institutions, but not spirituality. 
5. Move from debate to dialogue (we have WAY too much debate today): I don’t want to argue, let’s learn from each other. What can I learn from you and vice versa. I’ll be open to you if you let me be open with you. We can say who we are and who we follow if we follow this line and listen to the other.
6. Don't Manipulate ... Just Be Intentional: “I am a Christian, now can we move on?” Christ is not about manipulation. Move away from manipulating conversations and be real with people. Eventually, if the conversation authentic and we are sharing who we are, eventually we will come to a conversation about our faith. It is central to us and will come up if our conversation partner is serious about knowing who we are. Let the conversation develop naturally. Don’t be ashamed of the Gospel. Be authentic. Be aware of natural opportunities to share who you are. That will come out in conversation naturally. With old evangelistic methods, we tend to have forgotten natural conversation. Relationships require a lot more work than handing out a tract, and are worth it. 
7. Tell what you know in story form: Tell people the story of particular moments with you and God. American Baptist Churches USA recommends you tell the story of what Jesus has done for you (or at least one little piece of that story). People respond much better to story than to canned remarks. 

For more on this subject, you can read the book: Jim & Casper Go To Church.