The New Testament arose out of a need for authoritative teaching on God and Jesus Christ. By the year 397 A.D., councils from Churches had agreed on the 27 books now forming the New Testament, and arrived at this decision based on the authority of the texts themselves.
Basically, any text unquestioningly ascribed to an Apostle of Jesus was included in the Canon; and any text unquestioningly ascribed to a disciple of an Apostle (e.g., Mark and the Gospel of Mark) was included.
There were several texts included that were not unanimously believed to have been written by such authors, but these texts received their inclusion as they: a) possessed self-evident authority; b) were not heretical (as based on Apostolic teaching); c) had been used extensively in part of the Church for some time; and d) were written within a relatively short period after Jesus' death, to ensure eye-witness authority.
This essay (in pdf form) explains in detail the process taken in the formation of the New Testament.