I could give a few reasons why the New Testament, for example, could be considered reliable.
The truthfulness of the Bible, and by extension, all of Christianity, can be reduced to the truthfulness of Jesus's resurrection. If Jesus really rose from the dead, then he was who he says he was. If he was who he says he was (the son of God), then the new testament is true. And since Jesus claimed the Old Testament was true, then if Jesus was God's son, it could also be assumed that the Old Testament is true as well.
The New Testament authors include details about the resurrection that they would have not made up, which includes embarrassing or shameful details about the gospel writers themselves. For example, Joseph of Arimathea, who was a member of the Sanhedrin (the Jewish group that wanted Jesus to be crucified in the first place) was the one to bury Jesus. This is peculiar, because the fact that the apostles allowed a member of the Sanhedrin bury Jesus shows that they were most likely humiliated due to the recent events, perhaps even their faith wavering (hence "doubting Thomas"). Another major detail about the resurrection that could be considered embarrassing was the fact that the first witnesses of the risen Jesus were women, one of which was formally demon-possessed (Luke 8:1-3). In those days, a woman's testimony was not considered credible in court of law. Therefore, if the New Testament writers wanted to purposely make things more believable, they would have said that a man was the first person to witness the risen Jesus, or better yet, one of the Apostles.
The New Testament includes over thirty historically confirmed individuals in their writings. Because these historical figured were alive during the actual events of the gospel, and during the writing of the gospel, it would have been absurd and possibly dangerous to include them in a made-up story because any of them could have debunked their claims easily.
Each of the Gospel writers also each include details in the New Testament books that vary, but not contradict each other. If the New Testament was a hoax, then they most likely would have met beforehand and made a conscious decision to be consistent in their writings as not to accidentally contradict each other. These divergent details actually help the New Testament's case, because it shows that each author noticed different things and wrote about what stood out to them personally. Just as different newspapers and television stations will report the same event different, the writers of the New Testament did as well.
Besides including actual historical figures in their writings, the New Testament authors also tell their readers to check out other verifiable facts pertaining to the events of the gospel. Paul claimed to the Corinthian people that the signs and wonders were done among them (2 Corinthians 12:12). Paul would not have said this if he were making it up, because why lie to somebody about something they themselves did or witnessed?
Another interesting detail about the Bible is that the writers describe miracles and other historical events with a relatively nonchalant attitude. If the gospel's authors were making everything up, then their descriptions of the events would most likely have been more fantastic or outlandish, see
The Gospel of Peter (an "apocryphal forgery"). It describes a very dramatized and embellished version of Jesus's resurrection. It is likely that if the New Testament were also a lie, the the descriptions given by the apostles would probably more closely resembled that of the one in
The Gospel of Peter.
The New Testament authors abandoned their Jewish beliefs in favor of Jesus's teachings. The decision they made to reject many of the 1,500-year-old Jewish traditional rules would have seemed strikingly ludicrous in those days. These rules were a part of their heritage, and culture. It is unlikely that they would have dropped it all to follow some kind of lie, let alone defend that under the threat of death.
There is evidence for the Bible that can be found outside of the Bible itself; particularly, eye-witness testimony from Christian, non-Christian, and anti-Christian sources. What is most intriguing is the admission by anti-Christian sources that Jesus did in fact perform supernatural acts and miracles, or as they called it, "sorcery". Interestingly, there are more extra-biblical sources that mention Jesus than there are documents that mention Tiberius Caesar. If you only look at these extra-biblical sources, you can essentially reconstruct the gospel's entire storyline.
The New Testament displays a remarkable amount of reliability compared to other historical documents. Plato's writings, which are often-quoted by historians and other scholars, have a 1,200-year gap between the actual time of writing and the earliest surviving copies. The New Testament, on the other hand, has only a twenty-five year gap between the actual event and the earliest known manuscripts.
The New Testament has twenty-seven different sources. More than any other ancient text. There are about 5,700 New Testament manuscripts in the original Greek language, and around 9,000 in other various languages in such as Latin. Early church leaders often quoted the New Testament; fascinatingly, nearly the entire New Testament, save for eleven verses, can be reconstructed from these leader's writings and transcriptions. There is also striking earliness of the New Testament documents. At least some of the books were penned just a few years after the death of Jesus, in the 40's and 50's AD. Some skeptics ask why there are not earlier documents. This is because some of the New Testament writers had hopes that Jesus would come back in their lifetime, and felt no need to write the story down.
To reconstruct the New Testament from its many sources, scholars compare the man manuscripts with each other, and because of the scribes' meticulous copying habits, the original text can be recovered beyond a reasonable doubt. Critics will often claim that the New Testament has about 200,000 errors. It must, however, be noted that strictly speaking, all of these errors are nothing more than grammatical variants and have little to no significance in the Christian faith as a whole.