One God, not three gods
The Bible is clear that God is one. Israel was called to worship the Lord alone, not a collection of competing deities (Deuteronomy 6:4). Christians hold firmly to that same truth.
At the same time, Scripture speaks of the Father, the Son, and the Holy Spirit in ways that cannot be reduced to three separate gods. The word Trinity does not appear in the Bible, but Christians use it as a short way of gathering together what the Bible teaches about the one God.
Hear, O Israel: The Lord our God is one Lord:
Three distinct Persons
In this phrase, Person does not mean three human individuals with separate bodies. It means the Father, Son, and Spirit are genuinely distinct from one another. They relate to one another, speak of one another, and act together.
Jesus' baptism gives a vivid picture. The Son is baptised in the Jordan, the Spirit comes down like a dove, and the Father's voice speaks from heaven (Matthew 3:16-17). This isn't one Person changing costumes. All three are present at once.
Jesus later tells his disciples to baptise people in the singular name of the Father, Son, and Holy Ghost (Matthew 28:19). One name, three named Persons. The mystery is real, but it is not a contradiction.
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: And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased.
Each Person is fully God
The Father is God, and Jesus speaks of him that way (John 6:27). The Son is also fully divine. John begins his Gospel by saying that the Word was with God and was God, then identifies that Word as the one who became flesh in Jesus Christ (John 1:1, John 1:14). Jesus also speaks of his unity with the Father (John 10:30).
The Holy Spirit is not simply God's power or an impersonal force. In the account of Ananias and Sapphira, Peter says that lying to the Holy Ghost is lying to God (Acts 5:3-4). The Spirit teaches, leads, and can be grieved, showing personal action rather than an abstract influence (John 14:26, Ephesians 4:30).
In the beginning was the Word, and the Word was with God, and the Word was God.
A mystery worth receiving
No illustration completely explains the Trinity. Water, an egg, and the sun may point to small parts of an idea, but each can easily suggest something Scripture does not teach. God is not three parts, and he does not move in and out of three roles.
Still, the Trinity is not meant to be a puzzle that keeps people away from God. It helps us see the God revealed in Jesus. The Father sends the Son, the Son gives himself for the world, and the Spirit brings believers into God's life and love (John 3:16, Galatians 4:6).
You don't need to solve every question before you can worship God. Read the passages slowly, notice Father, Son, and Spirit in their setting, and let Scripture lead your understanding.