Steve Ray has a list of 35 loaded Questions for "Bible Christians" (quotation marks his)(link to the whole list). This is number 9/35. I'm trying to provide the answers in a common format, for easy reference.
9) On what authority, or on what principle, would we accept as Scripture books that we know were not written by one of the twelve apostles?
We accept them on faith.
1) We know that the whole Old Testament was not written by one of the twelve apostles. We also accept them on faith.
2) The fact that we accept them on faith doesn't mean that our faith is irrational. Thus, for example, the following are also the case.
a) The Holy Spirit testifies to His word.
b) We have historical evidence that also supports our conclusion that a particular book or passage is Scripture.
c) But ultimately, "my sheep hear my voice" is the governing principle.