In Deuteronomy 6:4 we read “Hear, O Israel: The LORD our God is one LORD.” And this is foundational throughout the Bible, there is One God.
Right away when we start the New Testament we see there is something more to be understood.
Matthew 3:16 “And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him: 17 And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased.”
This was not the same Person. There was One speaking in heaven, One descending from heaven to earth, and One standing upon the earth. Should it be that each are called God, then you either have polytheism, or there's something more to this.
The Father said, "This is My Son, in Whom I am well pleased." The Father recognized that the Son was Someone other than Himself, rather, His Son.
Some other verses that speak of Father, Son, and Holy Spirit:
2 Samuel 23:2 The Spirit of the LORD spake by me, and his word was in my tongue.
Isaiah 7:14 Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel (God with us).
Isaiah 9:6 For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.
Matthew 10:20 For it is not ye that speak, but the Spirit of your Father which speaketh in you.
Matthew 11:27 All things are delivered unto me of my Father: and no man knoweth the Son, but the Father; neither knoweth any man the Father, save the Son, and he to whomsoever the Son will reveal him.
Matthew 16:27 For the Son of man shall come in the glory of his Father with his angels; and then he shall reward every man according to his works.
John 1:18 No man hath seen God at any time; the only begotten Son, which is in the bosom of the Father, he hath declared him.
So there clearly are Father, Son, and Holy Spirit
But then, each are called God:
Jude 1:1 Jude, the servant of Jesus Christ, and brother of James, to them that are sanctified by God the Father
John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God.
Acts 5:3-4 But Peter said, Ananias, why hath Satan filled thine heart to lie to the Holy Ghost, and to keep back part of the price of the land? Whiles it remained, was it not thine own? and after it was sold, was it not in thine own power? why hast thou conceived this thing in thine heart? thou hast not lied unto men, but unto God.
Each acts in the same capacities as God:
Creating:
Malachi 2:10 Have we not all one father? hath not one God created us?
Colossians 1:16 (speaking of Jesus) For by him were all things created,
Job 33:4 The Spirit of God hath made me, and the breath of the Almighty hath given me life.
Psalm 148:5 Let them praise the name of the LORD: for he commanded, and they were created.
John 1:3 (of Jesus) All things were made by him; and without him was not any thing made that was made.
Gives to us eternal life:
Romans 6:23 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
John 10:28 And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand.
Galatians 6:8 For he that soweth to his flesh shall of the flesh reap corruption; but he that soweth to the Spirit shall of the Spirit reap life everlasting.
Raised Jesus from the dead:
1 Corinthians 6:14 And God hath both raised up the Lord, and will also raise up us by his own power.
John 2:19 Jesus answered and said unto them, Destroy this temple, and in three days I will raise it up.
1 Peter 3:18 For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but made alive by the Spirit:
Everywhere at once (omnipresent):
Jereriah 23:24 Can any hide himself in secret places that I shall not see him? saith the LORD. Do not I fill heaven and earth? saith the LORD.
Ephesians 1:23 (speaking of Jesus) Which is his body, the fulness of him that filleth all in all.
Psalm 139:7-8 Whither shall I go from thy spirit? or whither shall I flee from thy presence? If I ascend up into heaven, thou art there: if I make my bed in hell, behold, thou art there.
Saves us:
2 Thessalonians 2:13 But we are bound to give thanks alway to God for you, brethren beloved of the Lord, because God hath from the beginning chosen you to salvation through sanctification of the Spirit and belief of the truth:
Titus 3:4-6 But after that the kindness and love of God our Saviour toward man appeared, Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost; Which he shed on us abundantly through Jesus Christ our Saviour;
1 Peter 1:2 Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied.
What I find in the Scriptures are that the Father, the Son, and the Holy Spirit are each individuals, each are God, and that there is only One God.
There are many ways people use to try to describe or understand this doctrine (teaching) of the Trinity, all fall short.
Much love!