When pressed to explain the Trinity by Muslims, Unitarians, and Jehovah's Witnesses, Christians have often retreated by saying that the Trinity is a mystery. That may preserve their faith, but it is hardly a viable explanation of the model.
The Trinitarian model is attacked as illogical by those who say that the idea is a contradiction in terms. One plus one can never make three. A facetious answer is that with God you do not add but multiply, and one times one times one times one still makes one.
A more helpful approach is to explain that we are all agreed about the oneness of God. But oneness is of many different kinds. In life nothing is simple. The oneness of the simplest atom is a proton, a neutron, and an electron held together by atomic force. In India I used to explain that the skin, and stone, and flesh of a mango do not add up to three mangoes.
As we talk to practising Christians from many denominations it seems that there is a typically Trinitarian Christian experience of God. We experience the Father as a loving parent so to speak above us. We know the Son as a friend, leader, healer, forgiver beside us, and we experience the Holy Spirit inspiring, guiding, giving wisdom, creating love, and praying (again metaphorically) from within us. Each of these experiences points to an eternal and essential complexity within the oneness of the God we experience.
How can we think of such complexity? We could begin by reminding ourselves that Christians all begin by explaining that God is love. And God did not begin to be love when our world was made. God was love eternally. But it is very hard to imagine the love of a single unitarian unit. That is why a Trinitarian explanation pictures a loving oneness of three persons in constant conversation and interaction with one another.
This is suggested powerfully in the very first chapter of the Bible. "Let us make humankind in our image, according to our likeness ... so God created humankind in his image, in the image of God he created them; male and female he created them" (Genesis 1:26,27). As we read the Bible we meet a God who cares and sets up our learning environment like a loving parent. Already in the Old Testament God was encountered as the Lord who calls us to serve Him, but also as Friend who wants to walk with us. And there are many references to God as Spirit inspiring and empowering people in the Old Testament, and doing the same for us at the depths of our very being.
In the New Testament the interrelated oneness of these three Persons is assumed in the account of the baptism of Jesus. The great commission to baptize and teach in the name of the three Persons of the Trinity is obeyed by Christians all over the world. It is also hinted at in other New Testament texts where the Father, the Son, and Holy Spirit are spoken of in one breath.
The early Christians took the idea of an interrelationship within the oneness of God for granted, presumably having learned to think of God in this way from Jesus Himself. See for example Matthew 3:16-17, 28:19- 20, Luke 1:35, Acts 5:30-32, 7:55, Romans 8:9-17, 2 Corinthians 3:13, Ephesians 2:18.