First of all, we hold that the Bible was divinely inspired, in other words, God wrote it through people. So at the end of the day, whatever human hands wrote Genesis, it was inspired by God. This is a critical part of our faith, see About the Bible.
Tradition holds that Moses wrote the book of Genesis and the other books of the Law, or Torah (Genesis-Deuteronomy). Yet clearly, Moses lived long after the creation accounts so he could not have written eyewitness accounts of creation. Thus it is likely
that there were several generations of oral tradition. Even this though is debatable, as written tradition may have existed earlier then Moses. Whether it was written or oral Moses is traditionally the one credited with putting the Torah together for the first time. It is important though that when we consider the idea of ‘oral tradition’ that we understand that it was a much more sophisticated tradition then we can comprehend. Our spiritual ancestors used very unique memory devices to ensure the proper passing of history from generation to generation. They sang songs, they wrote poems, and structured stories in a way that allowed them to remember. You’ll see the depth of details in places like the genealogies in Genesis 5.
One of the toughest things to understand is how the creation account could have been recorded, remembered, or understood. Rather then getting into the different areas of debate (between believers, and between believers and non believers) I would rather emphasize the fact that God was there, and he communicated with his people. That is important for us, and while it may be difficult for some of us to understand or swallow, it is also a great comfort to me that God does speak to his people, and inspire his people.