All biblical theology can be summarized in two statements:
1. GOD IS. That fact is declared in the first four words of the Bible (Genesis 1:1) “In the beginning GOD.”
2. HE HAS REVEALED HIMSELF. And that is the rest of the Bible in its entirety. It is all about Him. It is His revelation of and about Himself to His creation. Everything we need to know for faith and practice, He has revealed in His written Word.
If we can get these two statements firmly embedded in our minds, everything else falls into place.
And frankly, I think it is enough. Most of us have a hard enough time understanding, believing, and obeying what He has revealed. We don’t need more or new revelation; we just need to believe what He has already given us.
And He has given us all we need to know about Him. So when it comes to hard truths, that are beyond our human ability to understand, like the tri-unity of God, we don’t have the prerogative to decide, define, or explain it. According to God’s revelation, the Father, the Word, and the Spirit-- these three -- are co-equal and coexistent.
Churches and denominations divide over this doctrine because they try to explain it in terms that make sense in our own human dimension and with our finite understanding. It is possible that many (or possibly all) people or can be WRONG about any particular doctrines, but one thing is certain; THEY CAN'T ALL BE RIGHT!
And any of our foolish attempts to deny God’s triune nature or to explain it with stupid analogies (like water or eggs or…) are ludicrous; in fact, analogies are probably heretical, idolatrous, or blasphemous.
God’s ways are not our ways; His thoughts are higher than our thoughts; He is the creator and we are the creatures; He is eternal and we are finite; He is spirit and we are flesh, and He exists in dimensions that we cannot conceive. And He has not seen fit to reveal, to us, how that can be nor has He ordained that we should understand it. He has just declared it and ours is to believe it. Apparently, that's all we need to know or He would have revealed more.
It is probably over-simplified to just state that the One True, Eternal, Living God co-exists in three distinct persons. The Father is God. The Son, our Lord Jesus Christ, is God. The Holy Spirit, the Spirit of the Father and the Son, is God. And yet these three are coequal in glory, and power. But that's about as reverently and Scripturally accurate as we can get when describing the Trinity.
Remember - God is and He has revealed Himself. As for me, I will just accept, as truth, what He has declared. To disbelieve His Word is to deny Him.