Once you have demonstrated how a non-Christian worldview either collapses on itself or fails to account for life in the real world as we know it (or both), you can then present the Christian faith as the worldview that makes the best sense of reality. How do you do that? There are a number of angles from which you could approach the issue, but I have found John Frame’s approach (dependent on the ideas of Cornelius Van Til) to be a very good one. In his book Apologetics to the Glory of God, Frame makes an argument that goes something like this:
Only the Christian worldview can account for the way we instinctively live our lives in this world. We all presuppose that there are transcendent moral standards. Whether we say so or not, we all live as though there is some standard by which to measure actions that are right and wrong. Even those who profess to be relativists still render moral judgments that presuppose this kind of standard. Very few people will be willing to go so far as to say that Hitler’s ethic was nothing more than a personal preference of his, neither better nor worse than any other person’s ethic. To render a value judgment on the ethic of a person (and of a community of people who followed Hitler) is to make an appeal to an ethical standard that transcends all individuals and all communities. Therefore, I take it that most people believe in some kinds of moral absolutes, whether they particularly like that language or not. Those who can dehumanize themselves to the point that they refuse to render moral judgment on genocide will have to be pressed a little farther to find the point where they appeal to a transcendent standard, but eventually I would assume everyone has some sense of an absolute right and wrong.
Now, we have to ask where this sense of right and wrong comes from. If it is absolute, then it must proceed from some absolute reality, that is, something that is the basis for everything else. In other words, absolute standards do not proceed from finite, contingent, limited things. We could not have deduced a universal sense of right and wrong from, say, whatever laws the government of Sweden happened to pass last year. The government of Sweden is finite, contingent, and limited. We must look for some kind of absolute reality.
A major question we must confront is this: is the absolute reality we seek personal or impersonal? Atheists say absolute reality is impersonal; all things arise from impersonal matter. The vast majority of adherents to non-Christian religions say absolute reality is impersonal. The default mode of worship for mankind is a pantheistic kind of worship, where nature itself is deified. But if absolute reality is not a personal being, then it is not a being that thinks, chooses, values, prefers, and commands. It is just a being that IS. And it is a well-known logical fallacy that you cannot move directly from “is” to “ought.” An impersonal ultimate reality (such as that in atheistic materialism and pantheism) cannot be the source of absolute moral values. I believe this is one reason why most pantheistic religions ultimately conclude that evil is illusory. Pantheism is incapable of holding in place the binary opposition of good and evil, because that kind of opposition requires an intelligent mind to distinguish between the two and to place value on the good and direct hatred toward the evil.
So we are left, then, with the only other alternative: absolute reality must be personal. We are talking about some sort of god as the source of all moral values. But is this the “unmoved mover” of Aristotle, the head of the Pantheon of pagan mythology, Allah of Islam, or the Triune God of the Christian faith? Well, we can rule out all mythological pagan views, because their gods are not absolute but are subordinate to an impersonal Fate. As for the other views, we are basically left with a conception of God as absolute individuality (as in Islam) or as a unified being who is, nevertheless, a community of persons (Christian Trinitarian belief). How shall we decide which better explains reality?
I don’t believe the world makes sense apart from the Trinity. Think about it: we have already determined that absolute reality must be personal. But personality only exists in relationship. Love, which is widely regarded as the highest ethical value (for good reason), can only be demonstrated when there is another to receive it. A god who is an isolated monad (like Allah or Aristotle’s god) would actually be sub-personal. He/It would be incapable of love or true personality apart from creation, and thus he/it would ultimately be dependent on creation for the fullness of his/its own being. But if God exists eternally as a community of persons, then he would always exist in relationship. If God truly is love (1 John 4:16), then he must be love from eternity. His love must be inherent to his nature, not an accidental byproduct of the fact that he decided to create something. In other words, even if God had decided never to create anything at all, that would not detract one iota from the fullness and richness of love that is shared among the persons of the Trinity. The fullness of the self-existent God requires a doctrine of the Trinity, and only the Trinity makes sense of what we instinctively know to be true about the kind of world in which we live.
And it is out of the doctrine of the Trinity that the glory of the Christian faith proceeds, for Christians believe that God’s love for the world is not the love of someone who is needy and codependent. God does not look at the world and say, with Jerry MaGuire, “You complete me.” Rather, it is out of his self-contained fullness that God opens himself to the world and welcomes his creatures into the eternal fellowship of the Trinity. That means our relationship with God is asymmetrical: we are entirely dependent on him, but he is in no way dependent on us, for he is entirely self-sufficient.
I have taken ethics as the starting point for this discussion, but you could start in a number of places and arrive at the same conclusion. Just take something that all people know to be true at some level (even if they deny it with their words), show that they cannot live life in this world apart from such an idea, and then show how that idea rests on the assumption that the triune God is creator and ruler of all. Only the Christian faith can explain the world as we know it. Invite the unbeliever to wear your glasses for a minute and see if things clear up for him.