Through The Bible we learn that there is only one God, that He is a person, that He created us in His image, and that, above all else, He Loves us intensely. But, in the New Testament, we learn that Jesus, who is a man who walked among us on Earth, is also God and one with Him, and yet he also prays to Him. Furthermore, we also learn of the Holy Spirit who dwells inside of us who is also God. The logical question is, “If there are three of them, how can they be One? And how can that work?”
The way to explain this is tricky, because we have many ways of describing this, but none of them can quite explain every feature of the Trinity... and that's just fine! God is immeasurable and unknowable by us, which is a feature of being omnipotent and infinite. We can, however, begin understanding Him, much like a child begins to learn advanced calculus by counting the blocks on the playroom floor.
The Person of God
The first way and perhaps the easiest way of thinking of God is in relation to being a person. God the Father is the Mind of God. The Mind holds the intellect, thoughts, plans, and even, as I believe, a very interesting sense of humor, and leads the other parts in everything. We know this best, because our minds direct everything we do and make every choice of what the rest of us do.Jesus is the Body of God. He is the part that we can see and feel, and the part that goes out and does the work of the mind. This is significant as it was this part of God that was chosen to take on a human body, that His body may be connected to ours. We can think of this clearly when we tell our hands to do the work of our minds, like building a boat, hugging a child, or writing an article.
The Holy Spirit is the Heart and Spirit of God. He is the center of life and emotion of God. It is how we feel and communicate with God and Jesus. We have difficulty figuring out exactly how the Holy Spirit works much as we have difficulty figuring out how our own emotions work, even with our attempts of psychology and philosophy.
The Power of God
A shorter way to think of the Trinity is in terms of power and forces. God the Father is the Structure of the Power. It is the governing force and focuses them towards His plan. Jesus is the Action of the Power. He goes out to fulfill the plans of the Structure. The Holy Spirit is the Presence of the Power. It is the light and energy behind the others.
The Responsibilities of God
We might also think of the three parts of God in what they do. The Bible tells us in Revelation that they have many crowns which signify many responsibilities. We cannot know all of them, but we have been given some clues to what things each of Him do. God the Father is the one who orders and designs. Jesus is the one who goes out to serve and save and, some day, to conquer. The Holy Spirit is the one who teaches, empowers, and dwells within.