Trinity for Dummies:
This is very simple:
First, we all agree that the Father is God, so I will not bother to proof that.
Second, the Bible is explicit that Jesus also is God. In John 5:18 we are told that Jesus’ opponents sought to kill him because he "called God his Father, making himself equal with God."
In John 8:58, when quizzed about how he has special knowledge of Abraham, Jesus replies, "Truly, truly, I say to you, before Abraham was, I AM"—invoking and applying to himself the personal name of God—"I AM" or YHWH (Ex. 3:14). His audience understood exactly what he was claiming about himself. "So they took up stones to throw at him; but Jesus hid himself, and went out of the temple" (John 8:59).
Perhaps most important are passages that apply the title "the First and the Last" to Jesus. The "First and the Last" is an Old Testament title of Yahweh: "Thus says Yahweh, the King of Israel and his Redeemer, Yahweh of armies: ‘I am the First and I am the Last; besides me there is no god’" (Is. 44:6; cf. 41:4, 48:12). This title is directly applied to Jesus three times in the book of Revelation: "When I saw him [Christ], I fell at his feet as though dead. But he laid his right hand upon me, saying, ‘Fear not, I am the First and the Last’" (Rev. 1:17). "And to the angel of the church in Smyrna write: ‘The words of the First and the Last, who died and came to life’" (Rev. 2:8). "Behold, I am coming soon, bringing my recompense, to repay every one for what he has done. I am the Alpha and the Omega, the First and the Last, the beginning and the end" (Rev. 22:12–13). This last quote is especially significant since it applies to Jesus the parallel title "the Alpha and the Omega," which Revelation earlier applied to the Lord God: "‘I am the Alpha and the Omega,’ says the Lord God, who is and who was and who is to come, the Almighty" (Rev. 1:8).
So that wraps up number 2, that Jesus is God.
Third, the Holy Spirit is God. The Bible is pretty clear on that in 1 Cor. 2:10–13, Acts 5:3–4, 28:25–28, and many other places so I won't go into depth on that one here.
THEREFORE: Since the Bible clearly teaches that Jesus is God (cf. John 8:58, 10:38, 14:10; Col. 2:9), and it also clearly teaches that the Holy Spirit is God (cf. Acts 5:3–4, 28:25–28; 1 Cor. 2:10–13), and since we all agree that the Father is God, and at the same time we know there is only one God (Mark 12:29, 1 Cor. 8:4–6, Jas. 2:19), the only way we hold all four truths is by saying that all three are one God.
HOW IS THAT POSSIBLE?
We have to grasp the difficult concept that one being does not necessarily equate to one person.
A cat or a dog is one being and NO persons. A bird or a fish is one being and NO persons. A human is one being and ONE person. God is one being and THREE persons.
"Being" refers to what we are. "Person" refers to who we are. God, the Bible states, is Father, Son, Holy Spirit. WHO he is is three persons. WHAT he is is one God.
** Also, those who deny the Trinity usually also deny the Divinity of Christ, and this too is an old heresy