The list below is from the Resurgence and is focused on neighbors but most of the principles apply to non-believers in general:
1. Find a road that leads to Jesus.
In the course of conversation, be thinking of how Jesus intersects with the discussion, because Jesus intersects and touches everything in our culture: sports, music, art, politics. Look for bridges to introduce Jesus into the conversation. It should be just as casually or passionately as you talk about everything else.
2. Donʼt be weird and awkward.
“So…now, I'd like to talk with you about Jesus.” If all of a sudden you put on your “Jesus” hat and you are talking to them like a project and not a friend, then you’re entering awkward territory. Now, there will be times it becomes awkward because talking about Jesus and sin can be that way, but don’t let it be because you are socially weird.
3. Be winsome.
Included in that word is the word “win.” Be “winning” friends and the conversation by being engaging, friendly, and kind. For more on being winsome, check out Soul Winner by Charles Spurgeon.
4. Counter stereotypes and caricatures of Christians.
Many urban, secular folks have a particular caricature of a Christian, which is not very flattering (judgmental, harsh, the “morality police”), although many don’t personally have any Christian friends. Be gracious and talk with them, serve them, and love them.
5. Host an open house.
When my wife and I moved into a new apartment building we hosted an open house for the whole building and went over the top with really good food and wine. Dozens of our neighbors came out and it was the foundation for future gospel-centered conversations.
6. Be honest about your struggles and failings.
We all fall short. We all struggle and fail. The credit has to be given to Jesus in your life. Many non-Christians donʼt want to talk with Christians as they will feel guilty regarding their own problems.
7. Actions also communicate.
Serve your neighbors. Serve your neighborhood. Look for opportunities without being an attention-getter. Your neighbors are watching you and just as James said, faith without works is dead.