The New Testament is Trustworthy
I strongly urge you to read a substantial amount of the New Testament. By far, the strongest argument for the authenticity of the New Testament is the New Testament itself. For the most part, my arguments below merely highlight this or that passage from the text. Assuming that you are a skeptic, you should start with Luke and Acts, which were written by the same person. You should then read Romans and Corinthians by Paul. These writings are the easiest for non-Christians to read and understand. After you read those, the order that you read in is less important.
Wrote History, Not Fiction or Myth
Some people would assert that the New Testament is a fictional or mythical work. Christ did not exist; or if he did, he did not rise from the dead. The writers of the New Testament knew this, and the writing has been misinterpreted ever since. The writers were not dishonest, but they did not realize that people would blow the story way out of proportion.
This standpoint does not hold water because it does not agree with the actual writings. Regardless of whether or not Christianity is true, the authors of the New Testament want us to believe that it is. Here are some explicit examples. The first is the introduction to Luke.
I too have decided, after investigating everything accurately anew, to write it down in an orderly sequence for you, most excellent Theophilus [friend of God], so that you may realize the certainty of the teachings you have received. (Lk 1:3-4)
Here, Luke is explicitly claiming that he is writing history. There is no other reasonable way to interpret this line.
The second example is Paul's letter to the Romans (Rom 1:1-7). Paul makes an explicit summary of the critical events of the Gospel, including the resurrection. If the Gospel is just a teaching story, it would have a much less prominent place in this letter. However, it is clear from the location of the summary that the events are the most important topic in the letter. Without the events, the letter would not have much reason to be written.
Also, when you read the Gospels, they read as realistic renditions of what occurred. In many places, there are descriptions and events that are not necessary. The only real reason to put them in is because they happened.
After Jesus is arrested, an unknown young man is following them, wearing nothing but a linen cloth (Mk 14:43-52). They seize him, but he left the cloth behind and ran off naked. The young man is not named. Why would the author include this unless he or his source knew that it happened? This line has an intimate eyewitness feel to it. It is not central to the storyline, but it is the sort of color that an eyewitness would remember.
After a crowd asks him what should be done with an adulterous woman, Jesus writes in the dirt like he is thinking and stalling for time (Jn 8:1-10). The Gospel does not say what he is writing. It is not clear whether the writing is important or not. Jesus's point "Let the one among you who is without sin be the first to throw a stone at her," does not depend on whether or not he wrote in the ground. The only reason to include this is that it actually happened.
Finally, the Gospels lack mythical hyperbole. Myths are not afraid to blow everything out of proportion. In the Gospels there are many miracles, but they happen in a matter of fact fashion. Angels don't swoop in to fancy pyrotechnic displays. They just appear or are calmly sitting down. When Lazarus is raised from the dead (Jn 11:1-44), nothing is more striking than how understated the description is. If this was myth, we should expect this event to have a lot more elaborate imagery, which was the special effects of those days. A man is getting raised from the dead, after all.
So now we know that the authors of the New Testament wanted us to believe that what they wrote actually occurred. Therefore, it did occur, they were mistaken, or they were liars. Let us look at these other possibilities.
Next, we consider the possibility that the authors knew the true story, and intended for the work to be received as history, but were liars. There are two key problems with this position. The first is that the writers are spreading the words and actions of Jesus, and it is impossible to image the Jesus of the New Testament approving of such a fabrication. You cannot serve Jesus (whether he is real or imaginary) by lying in his name.
Second, almost all of the authors of the New Testament were martyred. Those who survived had no reasonable expectation that they would survive. Why would they die for something that they themselves did not believe in? If they knew that there was no reward in heaven for their actions, martyrdom is positively irrational. We have record of disciple after disciple remaining defiant till the end.
The authors believed what they wrote to be true. We now only have two possibilities. Either the New Testament is the work of honest observers of real events or the authors, honest men though they were, were deceived or mistaken.
There are some questions we must ask to determine if the authors were mistaken. Once we complete the questions, it will not be reasonable to say that the authors were mistaken.
How Close Were the Authors to the Actual Events?
The vast majority of the New Testament was written in the second half of the first century. It was complete by A.D. 150. Only a few of the authors were eyewitnesses, but the story can always be traced back to the eyewitnesses.
Is This Close Enough to Consider These Accounts Reliable?
The answer is yes. The eyewitnesses had to pass on the story before they died, of course. The eyewitnesses would not garble the story in a way that destroys the critical themes and events of the story. When you are seventy, do you forget why you married your spouse? Remember that Jesus was the most important thing that happened to them. They would be more likely to forget their love of their spouses than they would be to forget the words and deeds of their Lord. Now, that is not to say that they never made a mistake. I know that my parents argue about the details of conversations from two months ago, let alone forty years ago. Also, it is possible that they might occasionally disagree about something important from when they were young.
The situation is similar for second and third generation Christian authors. They finished writing by A.D. 150. Even though they did not see the most important event of their lives directly, it was still the most important event of their lives. It radically changed who and what they were when they learned of Jesus. They then devoted their lives to learning about Jesus and writing about him. They also had the entire Christian community to guide them. Because they were writing very soon after the events, the apostles and the apostles' immediate followers were still around to correct them. Again, it is expected that details may get altered in translation.
So, the question becomes, how do we know when the account is reliable? There are two requirements. The first is that the event must have been important. People tend to forget things that were not important at the time, so it would not be surprising if there were some mistakes here. All of contradictions in the New Testament that I know about are in the not important category. The second is that the event should be consistent with the person of Jesus from the rest of the New Testament. It is reasonably possible for two people to disagree about an old, but important, event; but if three or four agree, it is highly unlikely that the event is misconstrued in a meaningful way. Even if there is only one source on an event or saying, if that event or saying agrees with the person of Jesus found elsewhere in the New Testament, there is no good reason to disbelieve it.
In conclusion, the authors were men who indirectly witnessed extraordinary events that dramatically changed their lives and the world. It was the events that made the men, and not the men that made the events. There is no room for these men to be deceived about the events because of their closeness to them and because of how deeply they were affected by them.
Are There Other Sources That Were Equally Close or Closer That Give a Contradictory Account?
There are contradictory sources. Most of these are referred to as Gnostics. Dating these tends to be more difficult, because none of the church fathers support their authenticity. In some cases, we can say that they were written before a certain date, because a specific text is disparaged by a specific church father. Many of them were written within two centuries of Jesus's life, so they are early enough that we cannot throw them out immediately.
Are the Contradictory Accounts More Believable?
The reason that I don't expect to ever study these writings in detail is that they fail the tests that the canonical New Testament pass. The gnostic accounts are simply not believable, which is the primary reason that they did not get accepted into the New Testament. It is readily apparent when you read these alternate Gospels that the authors are writing myth, are liars, or are being deceived. To give one example, there is the Gospel of Peter. It was probably written around A.D. 125, but some believe that it was written earlier. To quote William Lane Craig:
In this account, the tomb is not only surrounded by Roman guards but also by all the Jewish Pharisees and elders as well as a great multitude from all the surrounding countryside who have come to watch the resurrection. Suddenly in the night there rings out a loud voice in heaven, and two men descend from heaven to the tomb. The stone over the door rolls back by itself, and they go into the tomb. The three men come out of the tomb, two of them holding up the third man. The heads of the two men reach up into the clouds, but the head of the third man reaches beyond the clouds. Then a cross comes out of the tomb, and a voice from heaven asks, "Have you preached to them that sleep?" And the cross answers, "Yes." (Apologetics: An Introduction p. 189)
Just like the strongest defense for the New Testament is the New Testament, the strongest argument against the alternate Gospels is the text itself. This passage has all the characteristics of a legend. It is fanciful and not believable. The other alternate Gospels are similar, to greater or lesser degrees. To a large extent, the tests I've given to prove the New Testament reliable are the same ones that the church fathers used to determine the canon, so it is not surprising that we get the same result.
We now know that the authors were writing about historical events, were not liars, and were not mistaken. Therefore, we should trust the authors just as we would trust anyone else with the same qualifications. Before I leave this section and discuss Christian doctrines that can be found in the Bible, I will discuss the topic of contradictions.
How to Deal with Contradictions
Atheists will often find hundreds of contradictions in the Bible, and then will proceed to state that this renders the Bible invalid and false. Fundamentalists will find zero contradictions and consider this to be a proof of divine authorship. How can two groups of people find such a different result when presented with the same Bible? The reason is that they are using a different method of determining whether or not there are contradictions, even though they seem to agree on what contradictions mean. That is, they agree that no contradictions make the Bible divine and true and contradictions makes the Bible false. Therefore, atheists and fundamentalists will expend a huge amount of energy debating this or that contradiction.
An atheist will call something a contradiction if a resolution is not immediately obvious to the casual observer. The atheist then declares both statements false. The first fallacy is that just because something contradicts at first impression does not mean that a more careful analysis of the data will give a contradiction. Secondly, if two things contradict, there are actually two possibilities. Either both false or one of them is true.
A fundamentalist will say that the contradiction can be removed by some (often drastic) stretching of our understanding of the two passages. A fundamentalist will then state that the inability to find a contradiction is another proof of divine authorship. The first fallacy is that people can be endlessly inventive. It is amazing what contradictions can be removed by enough creative rethinking of the data. The second fallacy is that just because two things are consistent, it does not prove (or really even imply) that they are both true. They could easily both be false.
The described methodologies of atheists and fundamentalists are ridiculous and would never be thought of value regarding any non-Biblical inquiry. Instead, we must answer two questions: "How do we know when there is a contradiction?" and "What do we do about it when we find one?" The answers are straightforward. We have source A, which appears to contradict source B. Let us imagine that source B does not exist. What does source A tell us after careful study? Then let us imagine that source A does not exist. What does source B tell us after careful study? Does source A alone completely agree with source B alone? If it does not agree completely, how completely does it agree? Using this test we find that there are indeed contradictions in the Bible. Now, what do we do with these contradictions? First we note that even if we throw out all the contradictory statements, we are still left with the vast majority of the Christian beliefs; and we are definitely left with all the central doctrines. Then we take contradictions one by one. For example, after the resurrection of Jesus, each of the authors gives a different person seeing Jesus first. If we only had one source, we would probably state with confidence who saw Jesus first. But because we have multiple accounts, we might assume that information has been lost. If we take it at face value, there is a clear contradiction. However, it is likely that Jesus met all the people in question, but each author recorded those visitations and ordered events to highlight the author's intended message. Another contradiction is how in the synoptics, Jesus almost never says "Amen, Amen I say to you," with two amens while he almost always does in John. In current writing exact quotes are the norm. However, in ancient written and oral traditions, variations in quotations are allowed, even expected, based upon the truth that the writer wishes to reveal. In John, this phrase is a synonym with, "Pay attention, what follows is important." This phrase gives the reader an outline of key points. Another example of a contradiction is the question of who bought The Field of Blood. Acts 1:18-20 indicates that it was Judas, while Mt 27:6-10 indicates that it was the chief priests. Any removal of this contradiction requires a rather strong stretching of what is written, which implies that at least one of the passages is historically inaccurate. However, who handed the money to the landowner and under exactly what circumstances is less important than the message of each evangelist, both of whom sought to show Judas's death as the fulfillment of scripture.
We must realize, though, that the existence of contradictions does mean that we must be careful not to take a single section out of context and hold it up as the final word on the matter. For now, we should read the Bible as the words of honest men who were reasonably close in time and distance to the actions and words of Jesus. These men are capable of making mistakes about non-vital details, and it is conceivable that they could make a mistake about an important detail or two. In order to believe, beyond a reasonable doubt, that something in the New Testament is true, we must see a pattern of verses with minimal contradiction. At it turns out, this is the case for every vital Christian doctrine. Of course, I must demonstrate these one by one. This will be the approach for this book. However, note that after we see with eyes of faith, a more God-centered understanding of scripture is more appropriate.
 The arguments in this section borrow heavily from Kreeft and Tacelli, Handbook of Christian Apologetics, Chapter 8. That chapter deals mainly with the resurrection, but the arguments pertain to the New Testament as a whole.
 To see this point argued by a master, see "Modern Theology and Biblical Criticism," by C.S. Lewis. This essay is available in Christian Reflections and Fern-Seed and the Elephants.