I've had my share of spiritual conversations, and I've been audience to a few as well. I have found that being a faithful follower of Christ is often as much about how you answer as what answers you give.
When engaging a person who doesn't claim to be a Christian, they will almost always have reasons. Some will be well thought out, like the problem of the existence of evil. Some will be less so, like "I just don't think much about that sort of stuff". Some will be historical, like the Crusades and witch trials. And still others will be emotional and experiential, like the personal experience of being browbeaten by a Christian parent.
What ever the case may be, we are always presented with a choice of how to respond to challenges, doubts, questions, and criticisms of Christianity. In order to stimulate some self-reflection, I'd like to discuss a couple of the ways one may respond:
Retreat. This is often the path of least resistance. I've been guilty on more than one occasion of simply biting my tongue when I didn't even want to involve myself in a conversation. While Christ and his followers were metaphorically smeared in the mud, I stood idly by. This can be a tempting course especially if one is new to Christianity or feels unprepared to talk about their faith. While I personally devour any book on apologetics (the defense of the faith), one doesn't have to be well-versed in all the arguments for Christianity to get involved. Often a personal account of a life changed is more powerful than a book full of arguments. Of course, there are times when not saying anything can be the most effective witnessing tool. However, I've found St. Francis of Assisi's quote "Preach the Gospel at all times, and when necessary, use words" as an easy excuse for those too lazy to read up or too afraid to speak up.
Retaliate. This is returning challenge for challenge, and intensity for intensity. Retaliation lies on the other end of the spectrum from retreating from a conversation. I've seen conversations go bad very quickly as a "defender of the faith" burns all their bridges by being defensive, aggressive, close-minded, or just plain hateful. Retaliation can rear its ugly head in many different ways but it is characterized more by the tone and intent than by the content. For just one example, there is a way to discuss the reality of hell, and many ways not to. While, at times, retreat can be a proper response, I've never seen retaliation used well.
Reject. This seems to be a popular angle in today's culture. Since Christianity is getting such a bad rap, I'll just reject what ever is most offensive and keep the rest. This can be as simple as rejecting the title of Christian ("I'm not a Christian, I am a follower of Jesus"). Or it can be the rejection of orthodoxy and parts of Scripture that don't sit well with us or others (like the rejection of hell resulting in the rising popularity of universalism). The question of whether rejection is a good approach or not lies squarely upon what it is you are rejecting. While I don't have a problem with it in principle, you can only reject so much of what is offensive about Christianity before you are either forced to reject Christianity altogether or resort to the last response.
Reform. While changing a person's heart is in the hands of God, we can often help remove some of the roadblocks in a person's mind. This is rooted in reforming a person's concepts (or more often misconceptions) of Christianity in a way that is winsome, honest, humble, and gracious. For instance, every time someone wants to bring a laundry list of Christian tragedies (from the Inquisition to Ted Haggard and everything in between), I carefully remind that one can't judge a belief on its abuses. In fact, against most criticisms and challenges, I find the life of Christ to be the most compelling answer on almost every level (historical, spiritual, existential, etc.) I see my role as simply one of removing myself and as many misconceptions as I can out of the way so that they may see the beauty of the gospel.
"Conduct yourselves with wisdom toward outsiders, making the most of the opportunity. Let your speech be seasoned with salt, so that you will know how you should respond to each person." Colossians 4:5,6