Many excellent books have been written on Biblical criticism, for example, 'Who wrote the Bible?' by Richard Elliot Friedman (buy it here), and it is a subject widely taught in universities. 

(Click here for a list of logical fallacies and inaccuracies in the first 88 pages of Friedman's book)

It turns out that basically all Bible criticism is based on one of three things; archaeological evidence, linguistics, and science.

This is a much longer discussion, but in brief:

a) Archaeological evidence:

Archaeology is by nature fragmentary, incomplete, and open to interpretation. We're not really sure what anything we find is, especially not in context, we also don't know what we'll find next to fill in the gaps, our dating system is inaccurate and often you wouldn’t expect to find archaeological evidence for things (for example a nomadic tribe in the desert for 40 years wouldn’t leave any trace, anything that was left over would be buried several kilometres under the by now. Read this.

b) Literary, linguistic factors:

The leading theory in this field, the Documentary Hypothesis (in fact Hypotheses plural seeing as there is no consensus amongst the several different propositions of this criticism), proposes that the Torah was derived from originally independent, parallel, and complete narratives, which were subsequently combined into the current form by a series of redactors. We can see this, apparently through the repetitions, different styles, seeming contradictions, different genres etc that appear in the text. 

Textual criticism comes to demonstrate that the Torah can not have been the work of ONE HUMAN AUTHOR (OHA). (Although we have texts known to be written by one author with more variations than in Genesis) 

However - this says nothing to the claim that the Torah was written by ONE DIVINE AUTHOR (ODA) - who is not bound by human psychology or literary styles. We infact can’t suppose or expect anything from Gd and how He would choose to write his book. It renders all Biblical criticism based on textual analysis completely irrelevant. See here for a one page, thorough refutation of this hypothesis. 

c) Science: 

The science vs. religion debate continues unabated, with no decisive proof either way. For those of you interested in learning about the opinions that say Torah and science are not in conflict at all, and even how science is now coming to bring evidence for the Torah view of life, you can check out the work of Dr. Gerard Schroeder — a Ph.D. physician from MIT (buy one of his many books, Genesis and the Big Bang here) or Steven Meyers Return of the Gd Hypothesis (buy here). Needless to say, these works have their critics; as I said, the debate continues. Having done a lot of research on the matter, I have come to the rational conclusion that there is no way the intricate make-up of the world and all the organisms therein could be random and also that there is no way that consciousness can arise from matter. (YouTube Don Hoffman’s groundbreaking research on consciousness).