Who authored the Scriptures?

41 Now while the Pharisees were gathered together, Jesus asked them a question, 42 saying, “What do you think about the Christ? Whose son is he?” They said to him, “The son of David.” 43 He said to them, “How is it then that David, in the Spirit, calls him Lord, saying,

44 “‘The Lord said to my Lord,
“Sit at my right hand,
    until I put your enemies under your feet”’?

45 If then David calls him Lord, how is he his son?” 46 And no one was able to answer him a word, nor from that day did anyone dare to ask him any more questions.  Matthew 22:41-46

In this passage Jesus is reasoning with the Pharisees about their expectations of who the Christ would be.  Jesus references Psalm 110:1 which was written by King David.  The Pharisees believed the Christ would be a man--and only a man--from David's lineage (that's why Christ is called "son of David") but Jesus questioned their understanding by showing that David, who lived multiple generations earlier than them, called Christ his Lord.  "The Lord (the Father) said to my Lord (the Son), 'Sit at my right hand, until I put your enemies under your feet.' "  David would not have called Christ his Lord if Christ was merely a man because the title "Lord" infers subjugation and you are not subject to people who live multiple generations after you die.  By calling Christ his Lord David showed he knew the Christ would be a God-man.

How did David have this insight?  Jesus says because David was "in the Spirit" when he wrote those words.  In other words, his words were not his own but they were given to him by the Holy Spirit. Peter provides more insight into this phenomenon as he explains why the apostles' testimony is dependable:

16 For we did not follow cleverly devised myths when we made known to you the power and coming of our Lord Jesus Christ, but we were eyewitnesses of his majesty. 17 For when he received honor and glory from God the Father, and the voice was borne to him by the Majestic Glory, “This is my beloved Son, with whom I am well pleased,” 18 we ourselves heard this very voice borne from heaven, for we were with him on the holy mountain. 19 And we have the prophetic word more fully confirmed, to which you will do well to pay attention as to a lamp shining in a dark place, until the day dawns and the morning star rises in your hearts, 20 knowing this first of all, that no prophecy of Scripture comes from someone's own interpretation. 21 For no prophecy was ever produced by the will of man, but men spoke from God as they were carried along by the Holy Spirit.  2 Peter 1:16-21

What this means is people put pen to paper to write the words we can now read as Scripture, but it was the Spirit who instructed them what to write.