Okay boys, I'm a young guy, I work as a lead miner, my wife is about to deliver our second baby. I have never been to church in my life. I go to the tavern on Friday and Saturday nights. I'm good looking and the bar girls alway hit on me. Once in a while I hook up with them. My wife is at home caring for our first child and doing housework.
For some reason, I've been wondering about my life and my family lately. Something, my conscience I guess, has been making me feel guilty about the things I do. I've been wondering if I'm living the way I should. What will happen to me when I die? My wife isn't a church goer either. What about her and my kids? Is there something after death?
What can you tell me?
In your hypothetical situation, I would start with Christ but do it via Creation. Rather than jump directly into Jesus and what a sinner you are, I would explain how the world could not have evolved. Anyone with even a basic understanding of probabilities can see how unreasonable it is to believe that life evolved from a Big Bang into this multitude of forms that we see around us. On top of that, the Big Bang requires things like Space, Matter, in addition to abstract and invisible forces like laws of chemisty, laws of mathematics, laws of motion, laws of energy, etc.
A devoted evolutionist is said to have admitted that the odds of evolution were similar to the odds of a tornado hitting a junkyard and perfectly assembling a 747 from the metal scrap. In other words, Evolution is ridiculous even though the world mocks us for saying it.
So, if I can make some headway establishing that there is a God, and He is so powerful that He can create this world that we see, then perhaps we can move to the next step and talk about how man is the crown of God's creation, and that all was created for our good pleasure. If I can get this far, then I've established that God created and loved mankind from the start.
After that, it gets trickier, I think, but I'm not the one who will do the convincing....only the Spirit can bring someone to faith, but the next step is to talk about the Fall, and why there is evil in the world, and why Christ was necessary. From there, the historical Jesus can be discussed both through the Scriptures and through the secular reports from history. If someone who does not know Jesus can see that there is proof that this Man really lived on earth, then Christianity can become real instead of a fairy tale.
I think it is unproductive to badger people, so this has to be done with a light touch. If this hypothetical person trusts that I have his best interests at heart, he's going to be much more willing to listen to what I am saying. The man in your example needs to be told that his conscience is God's way of telling him to stop his sinful behavior, but there is a lot of ground that needs to be covered before the man in your example will probably be ready to join a church. Then again, maybe not. One can never be sure of the reaction when one is confronted with Jesus.