One thing we see out around us is John 3:16. We see it on signs, at sporting events and other places. People seem to use it to remind us of Christ’s presence and his life and death. God gave his only Son so that those who believe might have eternal life. What we must remember, is that in John’s thought eternal life was the age to come, an age begun with Jesus’ death and resurrection. Of course, no idea of the age to come is possible without the Holy Spirit and his coming as the new age dawned. In this way, we can see that the gospel is meant to reflect the idea of the Trinity. I think we are all acutely aware that we believe in One God, three persons, but explaining it is beyond what is possible for us. It is hard for us to conceive that God is not material and who and what He is will come to light at some future time of our existence. What we do have is an experience of three persons, Father(or a parental being), Son and Holy Spirit. We know the Son at an appointed time entered the world to give his life so that creation could be restored to union with the Trinity. At the end of his time, the Son left(sent) his Spirit to keep alive his Word and to aid and inspire his followers as they proceeded to walk in the new life given by the Son. This is why we always invoke the Father, Son and Holy Spirit.
Theologians for centuries have written and speculated about God and Theology including the Trinity. Yet Thomas Aquinas after a lifetime of writing and after a mystical experience concluded his work was straw.
Faith is what is needed. We come to know God by faith and experience by opening ourselves to him. Christ physically comes in the Eucharist, but the Spirit abides in us if we permit and helps us form an intimate and positive relationships as we walk the path and the way of the new life given to believers.