Genesis is formally anonymous. However, the authorship of Genesis is inseparable from the authorship of the Pentateuch. The Pentateuch is a literary unit. So it would be artificial to consider the authorship of Genesis in isolation to the authorship of the Pentateuch as a whole. Other Pentateuchal books indicate Mosaic authorship. That, in turn, reflects back on Genesis.
This is reinforced by the fact that Genesis introduces many motifs which prefigure later developments in other Pentateuchal books. This implies the Pentateuch (or at least the "final form" of the Pentateuch) was the work of one hand. That would account for its thematic unity, and the author's apparent foresight–which is creative hindsight. Although he actually wrote the Pentateuchal books in chronological sequence, in his mind's eye he had the entire narrative arc in view. He mentally wrote the Pentateuch backwards, beginning with the denouement, and working back to events leading up to the denouement. Compositionally speaking, he knew where he was going before he got there. The process of execution is in reverse order to the process of planning. The Pentateuch is essentially one book with one continuous story.
It's possible that Moses had a scribe take dictation. After completion, the text would be deposited in the ark of the covenant. Mosaic authorship allows for post-Mosaic scribal updating here and there.
Liberals are alert to apparent anachronisms in the Pentateuch that seem to point to a later date, but that cuts both ways. They ignore anachronisms that point to an earlier date than their theory postulates, viz. the nomadic wilderness setting of Exodus–Deuteronomy.
In commenting on Genesis, I'll refer to the author as the "narrator" rather than Moses, because that's the role that Moses is assuming in Genesis.
Depending on whether we favor the early or late date for the Exodus, Genesis was written in the early to mid-2nd millennium BC. Interpreting the book doesn't depend on which date we choose, especially since all events in Genesis considerably predate the time of composition.
Assuming Mosaic authorship, Genesis was written to emancipated Jewish slaves in the Sinai desert. It filled in the backstory of their history as a people-group. It clarified the identity of the one true God. The God who delivered them from Egypt was the same God who made the world, saved Noah, and guided the patriarchs. The God who delivered them from Egypt isn't a local God or tribal God. He is not one God among many. Rather, he is the Creator of the world. All other concrete entities are creatures.
It's possible that Moses made some use of oral or written historical sources in Genesis. However, his knowledge of certain events was presumably the result of direct revelation.
Genesis is a flashpoint of controversy in the debate over the relationship between science and Scripture. Christians have a duty to believe whatever God tells us in his word. In case of conflict, Scripture trumps science. And there's a necessary place for defending the claims of Scripture.
However, exegesis shouldn't be distracted by extraneous issues. Exegesis shouldn't be shaped with a view to modern debates. An interpreter ought to try as best he can to clear his mind of modern concerns and assume the viewpoint of the original author and his target audience. When reading Genesis, we need to ask ourselves what would be significant to the original audience? What would stand out for them? We need to imaginatively project ourselves into their situation. Check our own concerns and preconceptions at the door. Leaving modernity behind is, in turn, the best way to revise and correct our prejudices in the clarifying light of God's word. We need to adjust our perspective to the narrator's perspective. See the world afresh through the eyes of the narrator, rather than superimposing our cultural reference points onto the ancient text.
Commentators use comparative ancient Near Eastern literature to interpret Genesis. To some extent this can be useful, but it's easily overused. The first task of a commentator is to interpret the text before him, not compare it to another text and use the other text as the frame of reference. Even if we assume that the narrator is interacting with common ancient Near Eastern conceptions, the question at issue is what that means to the narrator, and not what it might have meant to the authors and editors of comparative literature. We must interpret Genesis on its own terms, according to the narrator's own vision.
In addition, using comparative literature to interpret Genesis assumes we know how to interpret the comparative literature. So the exercise can quickly devolve into vicious circularity.
In my opinion, many scholars fail to put themselves in the situation of the narrator and the immediate audience. Fail to experience the world as someone living in the ancient Near East would experience the world. Their world was not a literary construct. There are many things that even prescientific peoples would be aware of. The methodology of scholars is often backwards. Instead of viewing ancient Near Eastern art or and literature through the world the author experienced, they view the world through the art or literature.
For further reading:
Hess, R. "Language of the Pentateuch," T. D. Alexander & D. Baker, eds. Dictionary of the Old Testament: Pentateuch (IVP 2003), 491-97.
Mathews, K. Genesis 1–11:26 (Broadman 1996), 42-46.
