The Triune God eternally exists in three persons—Father, Son, and Holy Spirit. It’s important to emphasize that Christians do not believe in tri-theism, or three Gods that are of equal power. As Deuteronomy 6:4 states, “Hear, O Israel: The Lord our God, the Lord is one.” Other heresies that must be avoided are modalism (claims there is one person who appears to us in three forms), Arianism (denies the full deity of the Son and the Holy Spirit), Subordinationism (Son was eternal and divine, but not equal to the Father in being or attributes), and Adoptionism (Jesus lived as an ordinary man until his baptism, then God adopted Jesus as his Son and gave him supernatural powers).
All persons of the Trinity are distinct in their roles yet equal in deity. For example, the Father spoke the creative words to bring the universe into being, but it was the Son, the eternal Word of God, who carried out these creative decrees (John 1:3). The Holy Spirit was also active, moving over the face of the waters (Gen. 1:2), manifesting God’s presence in creation (Ps. 33:6). In the work of redemption, God the Father sends the Son (Gal 4:4; Eph. 1:9-10), the Son obeys and dies for our sins—God the Father and Holy Spirit did not die for our sins. The Holy Spirit works in our life to counsel us and bring us to the knowledge of the Truth (Jn. 15:26), and the Holy Spirit regenerates our heart, sanctifies us, and empowers us to conform into the image of God (1 Cor. 12:7-11)
In the Old Testament we come to Genesis 1:26, where God said: “Let us make man in our image, after our likeness.” This plural verb suggests that God is speaking about His nature. Some have suggested that this passage is referring to God’s “plural of majesty” or to the many angels, but there are no Hebrew examples of monarchy imposed in the text and angels did not participate in the creation of man, nor were angels created in the image and likeness of mankind. In Isaiah 9:6 we read that the child to be born into the world will be called mighty God, which is reffering to the second person of the Trinity, Jesus Christ, who took on human flesh and dwelt on the Earth. In Isaiah 63:10 God says that his people rebelled and grieved the Holy Spirit, suggesting that the Holy Spirit is distinct from God the Father but equal in the divine nature.
In the New Testament, when Jesus was baptized by John the Bible says, “the heavens were opened and he saw the Spirit of God descending like a dove, and coming upon him; and behold, a voice from heaven said, This is my beloved Son, with whom I am well pleased (Matt. 3:16-17).” Here in one moment the three members of the Trinity are performing three distinct roles. For example, the Father is speaking from heaven, the Holy Spirit is descending from heaven upon the Son, and the Son is being baptized. Similarly, in Ephesians 4:4-6, the apostle Paul states, “There is one body and one Spirit, just as you were called to the one hope that belongs to your call, one Lord, one faith, one baptism, one God and Father of us all, who is above all and through all and in all.”
For more on this topic, see Wayne Grudem, Systematic Theology, 248).