Canonisation of the New Testament

Criteria

1. The message
Christ died for our sins and He was buried and raised the third day (1 Corinthians 15:3-8)

2. The authors of the message
The apostles and their associates were eye witnesses of the death, burial and resurrection of Christ (John 21:24-25, 1 Corinthians 15:3-8, 1 Peter 5:1, 2 Peter 1:16-17, 1 John 1:1-3).
While Luke is not an eyewitness of the acts and miracles of Jesus, he was a eyewitness to the acts and miracles of Paul the apostle. (Luke 1:1-4, Acts 2:32, Acts 3:15, Acts 4:20, Acts 4:33, Acts 10:39-42)
Criteria of an apostle - eyewitness and with us from the beginning (Acts 1:21-22)

Condition

1. Christians were persecuted
Being a Christian in those days meant persecution that may result in death.

Process

1. By consensus, not officially sanctioned in an official meeting
As in many things in Christianity, such as the spread of Christianity in the first 200 hundred years (done not with political blessing nor power of the military, but by unknown itinerary preachers).
the acceptance of the New Testament was by consensus, not dictated by an official authority.

2. Eyewitnesses
Eyewitness authority of Paul (2 Peter 3:15-16), the apostles and their associates were recognized from the beginning. Matthew, Mark, Luke, John, Acts, and the letters of Paul were accepted, but there were some uncertainties about the general epistles.
In AD 367 the first historical list of all 27 New Testament books were listed in 39th Festal Letter by Athanasius bishop of Alexandria. The quote below were taken from this article in Christianity Today:
QUOTE
Athanasius wrote the list to end disputes about such texts as "The Shepherd of Hermas" or "The Epistle of Barnabas" which long had been regarded as equal to the apostolic letters. He also silenced those who had questioned the apostolic authenticity of Peter’s letters or the Book of Revelation. Athanasius states that "in these [27 writings] alone the teaching of godliness is proclaimed. No one may add to them, and nothing may be taken away from them."
UNQUOTE

Reference:
Do We Have the Right Books in the Bible? | Grace Communion International
367 Athanasius Defines the New Testament | Christian History
The Case for the Eyewitness Status of the Gospel Authors | Cold Case Christianity
The Apostles Wrote the Gospels as Eyewitness Accounts | Cold Case Christianity
How Can the Gospels Be Eyewitness Accounts If They Include Things the Writers Didn't See? | Cold Case Christianity