Although the term "Trinity" is not used in the Bible to describe the relationship of Father, Son and Holy Spirit, Genesis 1 gives the first intimation of their oneness of relationship.                                  

In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters.   Genesis 1:1 NIV

Then God said, "Let us make mankind in our image, and in our likeness, so that they may rule over the fish in the sea and the birds in the sky, over the livestock and all the wild animals, and over all the creatures that move along the ground."  Genesis 1:26


It was well over a thousand years before the prophet Isaiah was given this to write:

For to us a child is born, to us a son is given,
and the government will be on his shoulders.
And he will be called Wonderful Counselor, Mighty God,
Everlasting Father, Prince of Peace."  Isaiah 9:6


I may be stretching things, but it seems to me from other studies I have done, that the four names given to Isaiah describe the Trinity:  

Wonderful Counselor (The Holy Spirit),
Mighty God (the Trinity),
Everlasting Father (God the Father),
Prince of Peace (Jesus).


Another 700 plus years passed before John wrote this in his Gospel:

No one has ever seen God, but the one and only Son, who is himself God and is in closest relationship with the Father, has made him known.
John 1:18 

Then John [the Baptist] gave this testimony: "I saw the Spirit come down from heaven as a dove and remain on him. And I myself did not know him, but the one who sent me to baptize with water told me, 'The man on whom you see the Spirit come down and remain is the one who will baptize with the Holy Spirit.' I have seen and I testify that this is God's Chosen One." John 1:32-34


Then, when Philip asked Jesus to show him the Father Jesus said:

Jesus answered: "Don't you know me, Philip, even after I have been among you such a long time? Anyone who has seen me has seen the Father. How can you say, 'Show us the Father'? Don't you believe that I am in the Father, and that the Father is in me? The words I say to you I do not speak on my own authority. Rather, it is the Father, living in me, who is doing his work. Believe me when I say that I am in the Father and the Father is in me; or at least believe on the evidence of the works themselves."  John 14:9-11


Then Jesus told his disciples that he would send them the Holy Spirit after he went to be with his Father.
As different versions of the Bible describe the Holy Spirit in various ways, I decided to use the Amplified version which covers most of them.

But I tell you the truth, it is to your advantage that I go away; for if I do not go away, the Helper [Comforter, Advocate, Intercessor—Counselor, Strengthener, Standby] will not come to you; but if I go, I will send Him [the Holy Spirit] to you [to be in close fellowship with you].
John 16:7 AMP

Then Jesus came to them and said, "All authority in heaven and on earth has been given to me. Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age.  Matthew 28:18-20


It seems good to me to end with a hymn of praise: The Doxology, Written by Thomas Ken in 1674

Praise God, from Whom all Blessings flow;
Praise Him, all creatures here below;
Praise Him above, ye heav'nly host
Praise Father, Son, and Holy Ghost.


by Carolyn Schmitt