From the very beginning of the church, the groups and people who received letters from the apostles recognized those writings as inspired by God. This was true of both the Old and New Testament. Prior to Jesus, the writings of the prophets were received as the Word of God. After Jesus the writings of the apostles were received as the Word of God. The individual churches who received a particular writing knew it was from God. Those writings were then passed around among the churches. In fact, several books of the Bible were not written to individual churches but to entire people groups or several churches in a particular region (for example, Matthew, Mark, John, Colossians, Hebrews, James, John, Peter, Jude, Revelation). Some letters were written to individuals, which were then shared with a single church and then passed on to other churches. (such as, Luke, Acts, Timothy, Titus, Philemon, 2 & 3 John).
The churches recognized these letters as inspired by God from the very beginning. This is made plain in 2 Peter 3:16. Peter says that Paul’s writings are sometimes hard to understand, and those who are unstable twist Paul’s Words, just like they do the other Scriptures. Peter considers Paul’s writings the Word of God, even though they are at times difficult to understand. In Paul’s letter to Timothy he quotes the gospel of Luke and declares it is Scripture. In 1 Thessalonians Paul claims his writings are the Word of God. The apostles knew they were writing God’s Word and they knew that other writings of the apostles were inspired Scripture.
Because of the way in which the New Testament was written and distributed, there were times when false letters claiming to be apostolic were passed around the church. Because the writings of the apostles were sent to churches spread across widespread regions of the Roman empire some churches did not receive copies of certain books until decades after the books had been written. At that later point, and often without apostolic oversight, churches and groups of churches had to be able to decide between the true Biblical books and those which were false. To help make this determination, the church identified several criteria to identify genuine Biblical books.
First, the book had to have apostolic authority. For a book to be Scriptures it was to have been written by an apostle or under the direct supervision of an apostle. Second, the book could not contradict books already recognized as Biblical. Third, everything contained in the writing had to be true. Nothing inspired by God would contain errors or fraudulent claims. Any book found to be erroneous was rejected as not genuine Scripture. Last, the book had to have already been accepted by the church. A writing that was not recognized in any church as Biblical could not suddenly be elevated to be upheld as Biblical. The writing had to be accepted as Biblical by those who received it before it could be accepted as Biblical by the church at large.
At no point in history did anyone have an official meeting with all the possible books in front of them and decide if those books were going to be considered as Biblical. History tells us a few specific books of the Bible were not recognized by all the church until later and after much consideration. Many false books were rejected by the church, on the local and regional levels. In the end the formation of the New Testament was not the result of men deciding which books belonged, but of God moving holy men to write His Word. The churches that received His Word recognized the marks of authentic, Divine truth and acknowledged such writings to be the Bible.