For this question, we highly recommend that you read one of the following in order to get a broad overview of the topic:

Read Chapter 7 ,You Can't Take the Bible Literally, in "The Reason for God" by Timothy Keller

Read Chapters 6&7 in "Questioning the Bible" by Jonathan Morrow

Read Chapter 4 in "I'm Glad You Asked" (Download Here, 41 pages)

Dr. Jonathan Morrow - assorted topics

Author and speaker Dr. Jonathan Morrow presents a simple argument for the Bible’s reliability based upon the person of Jesus of Nazareth.
Author and speaker Dr. Jonathan Morrow presents his “go-to” facts when in casual conversation about the reliability of the bible.
Author and speaker Dr. Jonathan Morrow presents recent discoveries in biblical research and the impact they can have in everyday conversations.

J. Warner Wallace – The Top Three Reasons The Bible IS Reliable

Dr. Dan Wallace on The Reliability of the Biblical Text

The context for this video is the number of "variants" in the original text of the New Testament. The New Testament was written in Greek and the various books were copied by hand from the beginning of the church so they could be shared. We do not have any of the original manuscripts. This process of copying has left us with almost 6,000 copies of the New Testament documents in the original Greek. The "variants" are the ways these manuscripts disagree with one another. It is often charged that since the number of variants is very large, the bible cannot be trusted. Dr. Wallace shares the nature of these variants and how they actually help scholars to accurately reproduce the text of the New Testament. 

Dr. Darrell Bock, Dr. Michael Kruger, and Dr. Andreas Kostenberger on Biblical Inerrancy

In this episode, Dr. Darrell Bock, Dr. Andreas J. Kostenberger, and Dr. Michael Kruger discuss the inerrancy of Scripture and encountering common challenges to the trustworthiness of the Gospels.

Dr. Darrell Bock and Dr. Dan wallace on the reliability of the new testament text

At SMU Dr. Frank Turek was asked, "How do we account for the errors of the scribes in the New Testament since these documents were handed down from one person to the next and what if these errors are not simple and interfere with the teachings of the scriptures.