My apologies for the delay in responding to your questions, but I hope you will forgive me. In fact, in the past few days I have had the opportunity to read and think some more on this very issue, and, as there are many people wiser and smarter than I, it's usually beneficial to absorb much from good sources.
You have inquired after naturalism and existentialism (I will assume atheistic, unless you elaborate), and it is a propitious pairing, for the two have much in common. I ask you to always bear in mind that the people who hold other worldviews than our own are first, made in the image of God, having His character, however poorly, impressed upon them; second, we never seek to win arguments for ourselves, only to win souls to Christ, and this we cannot do of our own power; third, by virtue of the 6.7 billion or so distinct worldviews on the planet right now, we are forced to find one out of many, which is done by making generalizations which, if properly thought out and articulated, may be useful, but are almost never normative or exhaustive.
Thus far the prolegomenon, on to the meat.
When a naturalist (hereafter NAT) or existentialist (hereafter EX) looks out the window, the world they see is fundamentally not-God. This is the bedrock of their faith (for faith it is) that there cannot, must not, will not, and could not be a God. This is the idea which drives their endeavors, though their paths diverge fairly quickly. For now, though, they walk hand-in-hand. They agree that the world which is seen must simply have been, or have come to be somehow. They agree that death is all there is, and man is but an atom among atoms, decaying and mutating at last. They do not think there is a soul (how can matter have a soul?), but the EX will perhaps cough a bit and say that, well, the mind of man is unique and superior, but no, nothing supernatural can be, and death is merely a disordering of highly ordered matter, which was bound to happen. At the graveside, the NAT may mourn the passing of a good investigator, a skilled colleague, a "good man", and the EX may shed a tear for the pictures left unpainted, the lives left untouched, and the joy un-had. Never, in their mourning, do they leave this earth, and if they look upon the sky, they can think only of the heavenly bodies, never of heaven.
However, the NAT and the EX are not the same, and they harbor mutual suspicions of one another, and may also have mutual appreciations without understanding what on earth the other is up to. The NAT says "Matter is all there is, and it spit me up as I am, therefore I shall be king over it." Thereafter, he may spend his days studiously taking data, making experiments, and expanding science (if he is so inclined), or he may throw caution to the wind, eat, drink, chase tail, and make himself king of physical pleasures. If "stuff" is all there is, and this stuff makes you feel good, why not? Bear in mind that there are many, many more unsophisticated naturalists than studiously scientific ones. However, the ranks of hedonistic naturalists are dwindling, as many of them take the leap to postmodernism.
For an historical example of hedonistic naturalism, take old Shanghai, drenched in opium, cheap women, cheaper killings, and almost any bauble or pleasure then available. I doubt if a single one of the pleasure-seekers therein would believe 1) God exists and is watching all this or 2) there is no real reality or structure to the world. Same story with a large number of the notoriously hedonistic towns across time and geography. This world is the best there is, so live it up. Eat, drink, and be merry, for tomorrow we may die. Yes, this is a shallow take on the worldview, but it is a seductive one, and it is definitely one face of the NAT.
The other major face of the NAT is found mostly in the sciences, and is perhaps the one you will have cause to dialogue with the most. From the starting point of "stuff", these people conclude that they should find out about it. If you live on an island, perhaps your best calling is to learn to cook fish. So, if you live in a purely material world, you decide that manipulating matter is the best (and perhaps only sensible) use of your time. If pigs do not exist, there is no point in learning about pork chops. This is why these NAT will often have no use even for a conversation about something they are convinced does not exist. The goal of these folks is to keep digging. The Stephen Crane poem about the man chasing the horizon (in Sire's chapter on Nihilism) is an excellent illustration. Feynman was content with asking the questions, even if they only led to more questions. It is, however, difficult to have any concept of reality if there is never a rock-bottom answer. Look around you in your school, you will meet these people.
The scientist has had many conversations with the theologian over the years, and they have often been poorly conceived and poorly executed on both sides. There have been two major issues with these conversations:
1) The theologian doesn't know squat about science, and wants to bind the scientist's hands from the get-go, so they can't ask "wrong" questions, and
2) The scientist thinks this conversation is a waste of his time, like a debate about unicorns, and doesn't know a bit of theology, and wants to know less than that.
You, sir, as an educated Christian, are not allowed to make these mistakes. A few very helpful acknowledgements may ease the frictions inherent in such a conversation. Recall that everybody, but EVERYBODY, thought the Earth flat and the planets moving on celestial spheres for a very long time. That was wrong. Science fixed that. Were all of the astronomers Christian? No. Are their results valid? Yes. Christians should value and appreciate the gradual release from ignorance that scientists (of all stripes) have afforded over the years. Realize the Christianity depends on facts. Submit to your scientist compadre that we depend on the resurrection of a man from the dead in Palestine in the first century AD. This is open for investigation, because it is a fact, and there is no fact which is off-limits. As you challenge this, though, consider also that science categorically refuses to consider the supernatural. This is a conscious decision. The scientist should realize this, and understand that his investigations are limited because of it. The thoughtful Christian and the thoughtful scientist are separated ONLY by faith in Christ. Nothing else in the created order is allowed to create that division, and no discussion will include the gospel if it does not come back to "You must believe on Jesus Christ raised from the dead to be saved."
The NAT is, however, very interested in creation. He wants to understand it, where it came from, and why and how it works. So does the Christian! Again, there are no facts off-limits, so we must be absolutely sure that we distinguish the facts in the Bible and its inspired character from our interpretations of them, no matter how time-tested or comfortable they are. Recall again, everybody was very comfortable with the celestial spheres. So go take a walk with the NAT and look at creation! You can arrive at the same facts, the same conclusions, and the same applications, but the NAT cannot ever tell you what it means.
This is the Achilles' heel of naturalism. It can collect and catalog and poke and peer, but it can never answer "Why?" without leaving its fundamental commitment to "stuff". This is very apparent in ethics. Sire walks through the example of cultural relativism- some things are wrong because they damage a culture, so the culture outlaws them - but these are not universally accepted, so which culture is right? What about cultures that subjugate other cultures? Why is preserving a culture a good thing? If it's all relative, it's a race to the lowest common denominator, which is Nihilism. The NAT needs the Christ who made all things good, who orders and sustains them, and whose character and law are the true standard of behavior for all men everywhere.
On to our friend the EX. His commitment is utterly unto himself. He alone may define value for himself. He alone may make his revolt against the NAT's world, defying the death and decay (until he, too, capitulates). The EX sees that there is no hope of getting immaterial "value" out of the material world, and he says "OK, then I, an atom of matter, shall say what is valuable, and I will be right for me." Thus, the existentialist denies ultimate, supernatural purpose, and seeks for it in what amounts to solipsism (the retreat into oneself, saying 'I am all there is'). The EX does not deny the material world, he does not escape it, but he rejects it! "It's not enough, and my mind shall make what I shall approve of." Thus, a lot of existentialists tend to be artists, musicians, creative people who want to be the change they want to see in the world. The EX will not begrudge the NAT his search into the world, but he will sadly sigh, for he has decided that meaning will never be found there. Meaning comes from the relationships we build, with ourselves and others. Thus, out of chaos, an attempt at value.
Existentialism was big in the fifties and sixties, but it hangs on in a very major way. Of the serious (Western) students that you meet at a university, probably about 40% will be naturalists and 40% will be existentialists. The party boys might be hedonistic naturalists or po-mo, and there may still be a few Deists and Christian Theists in the serious category (but Deists are not intellectually respectable these days). For the EX, was your choice right for you? Did it help you realize your potential? Did you build yourself up today?
Before you brush off EX as wishy-washy, realize that it is a very serious effort to create meaning in an absurd universe. The EX realizes that there should be more to life than a laboratory for capricious chance to play, and more than a sex-drugs-and-rock-and-roll Xanadu. The EX truly wants value, and will settle for feeling valuable. Here is where you can approach them. Every person IS valuable! God has given each one a soul that craves meaning, and craves relationship with Him. That is where value lies, in Jesus Christ, fulfiller of deepest needs, creator of inseverable relationship.
Hopefully this has been helpful. I apologize for the dearth of brevity, but I did not have a target for the length of this missive. Do read and re-read Sire where you didn't get it, it's good analysis, and well worth it.
Remember that a lot of the things we take for granted would have gotten you excommunicated or burned in the Dark Ages. Hooray, science!
There is no-one beyond the gospel, and no-one who cannot be told of Christ and the resurrection, but recall that it is a stumbling block to Jews and foolishness to Gentiles. Who is sufficient for these things? (2 Cor. 2:14-17)