The Baptism of Jesus was an action in which three of the four gospels record God the Father, God the Son and God the Holy Spirit together, yet in distinct forms. They also record how the Trinity used John the Baptist to fulfill Jesus’ baptism.
Like his birth, Jesus received baptism as an act of obedience to God the Father. Jesus said to John the Baptist, “It must be done, because we must do everything that is right” (Matthew 3:14).
The Holy Spirit acted by pointing out to John the Baptist that Jesus was the one of whom he prophesied would soon come. John the Baptist said, “I didn’t know he was the one, but…[God] told me, ‘When you see the Holy Spirit descending and resting upon someone, he is the one you are looking for” (John 1:33). This must have been quite an awe-inspiring moment for John. The Messiah was his very own cousin.
All four gospels record the Holy Spirit’s action of descending like a dove and rested upon Jesus’ shoulder. The first three (synoptic) gospels record God the Father’s actions—He found it necessary to open up the sky and publicly say, “You are my beloved Son, and I am fully pleased with you” (Luke 3:21-22).
It is interesting to note that the gospel of John seems to include a portion of the baptism account from the eyes of John the Baptist. But John the Baptist was beheaded long before the first-person quotes in John’s gospel were written down. So how was it written in first-person? It could likely have been from John the Baptist’s personal memoir. Craig L. Blomberg wrote, “Jesus’ followers may well have privately kept written notes, using a form of shorthand, while passing along the tradition orally in public.” 
H. Wayne House notes that John the Baptist had disciples of his own, who continued his ministry as far as Ephesus. James Jeffers points out that Ephesus was a main stop when one was traveling by land or by sea, and we know that there was a church in Ephesus (the book of Ephesians and the book of Revelation). One could then surmise that John the Baptist’s writings, if any, could have been preserved, copied, distributed and available for research, reference and quotation among different churches in which his disciples could have visited.
A closer look shows us that John the Baptist not only baptized Jesus, but did so through the work of the Holy Spirit and in obedience to the Son, who himself acted in obedience to the Father.