I'm reading David Male and Paul Weston's "The Word's Out: Speaking the Gospel Today" (BRF, 2013) which has some interesting ideas. I was particularly struck by Paul Weston's thoughts around whether evangelism should be outside-in or inside-out.
He points to how Jesus did evangelism which tended to be by telling stories, suggesting that one of the problems we have with evangelism is that we come it from the outside. We use an approach that tries to justify, or explain, what we are saying. He suggests that if we were to use the gospel's stories as the response to people's interest and questions that might be far more effective.
The suggestion is that when someone asks a question, instead of trying to give an answer that starts from the premise of what we think, we take an approach that links the question to something that Jesus said or did, He comments that this will help us to "cut straight to the chase" as it focuses thought and conversation on Jesus. It doesn't mean that further comment won't be needed, but it does give us the right starting point.
Weston suggests that if we are always asking ourselves how Jesus responded when faced with similar questions to the ones we face, that will help us to be centred on the gospel, and so to be working from the inside out. "Our evangelism courses training courses would be considerably enhanced (and far more productive) if we were to take the issues that have arisen in our own lives and those of our friends or colleagues and ask how Jesus addressed them."