The answer to your question is an oral history existed and was passed down to new generations of believers. Once written language developed this history was transcribed into the first five books of The Old Testament.

After that either the Prophets themselves wrote books or observers of the Prophets recorded accounts from a Prophet’s life. How and why a book was compiled into The Old Testament, I’m not sure. I believe the early Catholic Church chose the books that are included in the New Testament.