Did you ever stop to think how every illustration of the Trinity falls short of capturing its essence? One of the most popular ways of thinking about the Trinity is H20, yet even though it can be water, steam, and ice, it can never be all those things at once.
Although the actual word, Trinity, does not occur in the Bible, there are, of course, numerous references to the three different aspects of the Godhead. Jesus' baptism is perhaps the clearest depiction we have: Jesus' being baptized with the Holy Spirit descending as a dove with the Father's voice expressing his pleasure.
Consider the Athanasian Creed: "And the catholic faith is this: That we worship one God in Trinity, and Trinity in Unity; Neither confounding the Persons; nor dividing the Essence. For there is one Person of the Father; another of the Son; and another of the Holy Ghost. But the Godhead of the Father, of the Son, and of the Holy Ghost, is all one; the Glory equal, the Majesty coeternal. Such as the Father is; such is the Son; and such is the Holy Ghost. The Father uncreated; the Son uncreated; and the Holy Ghost uncreated. The Father unlimited; the Son unlimited; and the Holy Ghost unlimited. The Father eternal; the Son eternal; and the Holy Ghost eternal. And yet they are not three eternals; but one eternal. As also there are not three uncreated; nor three infinites, but one uncreated; and one infinite."
Ours is to stand in awe of the mystery, not solve the puzzle, (an idea of Methodist theologian, Justo González.) Our awe will lead to our worship. Paul's marvelous prayer for the Ephesians (found in Chapter 3) hopes for the them to fully know the triune God, that they may "grasp how wide and long and high and deep is the love of Christ, and to know this love that surpasses knowledge [...]" (NIV). God is love.