Carson, D.A., and Douglas Moo An Introduction to the New Testament - Second Edition. Grand Rapids: Zondervan, 2005. "New Testament Letters" Carson & Moo pp. 331-353
What is the “canon”? At first the word referred to a standard of faith. By the fourth century the term “canon” came to refer to a list of books that were considered authoritative Scripture. An important consideration in the study of canonicity is whether the canonical status or the functional authority came first. Carson and Moo explore that question first considering whether there was an authoritative list of canonical books of the Old Testament agreed upon by Jews prior to the first century. It does appear that there were canonical collections of the Torah and Prophets, though there seems to have been some doubt about identification of some canonical books. This suggests that canonicity is a matter of recognition of authority, rather than presentation of an authoritative list which will then be accepted because of the authority of those presenting it.
In studies of the New Testament books as referred to by patristic authors we see that the gospels and major Pauline letters are quoted very frequently, the rest of the New Testament is quoted less frequently, and other works that we know about are hardly ever quoted. We find a summary in Eusebius of Caesarea, who lived about 260-340.
p. 734 “In discussing the New Testament canon, Eusebius deploys a tripartite classification: the recognized books (homologoumena), the disputed books (antilegomena), and the books put forward by heretics in the name of the apostles but rejected by those Eusebius regards as orthodox. In the first category, Eusebius includes the four gospels, Acts, fourteen Pauline epistles (Eusebius includes Hebrews, though he is aware that the church in Rome did not hold Hebrews to be Pauline), 1 Peter, 1 John, and, apparently (though with some reservation) the Apocalypse. Eusebius subdivides the disputed books into those generally accepted (James, Jude, 2 Peter, and 2 and 3 John) and those that are not genuine (Acts of Paul, Shepherd of Hermas, Apocalypse of Peter, Epistle of Barnabas, the Didache, and, perhaps, the Apocalypse). The third category, embracing clearly heretical writings, including gospels such as those of Peter and Thomas, acts of Andrew and John, and similar writings (H.E. 3.25).”
How were writings recognized? First and foremost by conformity to “the rule of faith” (Latin regula fidei). Does the book conform to orthodox Christian truth? A second mark is “apostolicity, which as a criterion came to include those who were in immediate contact with the apostles” (p. 736). Wherever early Christians suspect a pseudonymous work they reject it. Finally, canonicity is recognized by widespread, continuous acceptance and usage. If the text is not generally accepted as Scripture, even if it fits the two other criteria, it is not recognized as canonical.
Carson and Moo conclude that canonicity is generally recognized, then codified in lists. We recognize canonical texts because of their long and consistent use within the Christian tradition, by their authorship, and by their apostolic content.