"(Jesus) came unto His own, and His own received Him not. But as many as received Him, to them gave He power to become the sons of God, even to them that believe on His name: which were born...of God" (Jn. 1:11-13).
Notice that one becomes a child of God by believing in Jesus! I don't believe I have ever heard a sermon on the Lord's conversation with Nicodemus, that included the rest of the third chapter. That is sad, really, because it records the "how" of being born again! And you would think it would be so obvious to preachers! Verse nine says, "Nicodemus answered and said unto Him, 'How can these things be?'"
The Lord's reply (Jn. 3:14-18) to him was the Gospel! Jesus had to die, and be raised up (v. 14)! In verses 15-18, John declares that it is faith in Jesus that saves:
"That whosoever believeth in Him should not perish, but have eternal life. For God so loved the world, that He gave His only begotten Son, that whosoever believeth in Him should not perish, but have everlasting life. For God sent not His Son into the world to condemn the world; but that the world through Him might be saved. He that believeth on Him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God."
Peter wrote: "Being born again...by the Word of God..." (1 Pet. 1:23). Paul wrote that being saved (born again) is the result of believing the Word of God (Rom. 10:17), and that it is that faith in God's gift, God's offer of salvation, that saves us (Eph. 2:8-9)!
Being born again is the result of faith in central character of Scripture: Jesus!