There is no tenet of Christianity that has caused more confusion or controversy than the doctrine of the Trinity. The range of thought among those who claim to follow Christ spans from an uneducated belief in tritheism, to a belligerent denial of the Trinity's existence, to an impassioned plea that not only it, but all fundamental Christian theology should be swept aside in a quest for Christian unity.
Simply stated, the doctrine of the Trinity can be presented as two logical premises:
1) There is one God.
2) This one God is revealed in Scripture as three eternally distinct persons - Father, Son and Holy Spirit.
To the first point, Christianity carries the mantle first borne by Judaism in stating that there is only one Creator of heaven and earth. However, the arrival of a certain carpenter from Nazareth changed everything. Although He walked the countryside feeding and healing the masses, He said some rather outlandish things. Germane to the topic at hand was His insistence that the God in heaven was His Father. In fact, He delineated God as a distinctly different entity from Himself over 200 times in the Gospels.
In the reverse, at Jesus' baptism, a voice came from heaven saying, "This is my beloved Son, in whom I am well-pleased" (Matt. 3:17), clearly delineating a difference between the Father in heaven and the Son in the Jordan River. And as His ministry was drawing to a close, Jesus stated that the Holy Spirit would be sent by the Father in His name (Jn. 14:26), and that He would not speak of Himself, but of Jesus (Jn. 16:13).
One God, but three distinct persons. However if one focuses so much on the fact that God is one that they forget that He is three, they are in error. Likewise, the one who focuses so much on the three that they lose sight of the One is also in error. To emphasize one over the other is to try to decide which blade of scissors is more important.
There are many who claim that the Trinity is a contradiction. It need not be if understood correctly. To introduce an analogy, it is almost the same to say that there is the concept of time, made up of past, present and future. The present is neither the past nor the future, but yet these three elements make up the concept we call time.
As it stands then, what differentiates true Christianity from the anti-Trinitarian sects is a matter of perspective. If the arrival of Jesus of Nazareth was earth-shattering enough to split time, then it must fundamentally change how a Christian is to view God.
Imagine a young father stumbling to the refrigerator in the middle of the night to get a glass of milk. In the darkness, he steps on something which shoots searing pain up his leg. On the way back to his bedroom, he makes a mental note to steer clear of where he was when he stepped on whatever he stepped on. The next morning he gets ready for work and on his way to the kitchen, he spies a Lego block on the floor. "Oh, that must be what I stepped on last night". Conversely, it would be blatantly illogical to say, "I didn't see that last night, so that can't be what I stepped on."
This is the fundamental difference between Trinitarians and anti-Trinitarians. Trinitarians see the light of the New Testament and use it to shine on the Old Testament - similar to how the plan of redemption is progressively revealed throughout Scripture. With this light, they can make sense of the statement by God, "Let US make man...(Gen. 1:26)", or the Hebrew word for God being "one" in the Shema (Deut. 6:4), being the same as the Hebrew word for Adam and Eve being "one flesh" (Gen. 2:24). Anti-Trinitarians view the Old Testament as paramount, and then try to cram all the statements about deistic distinction into a box that is much too small.
It is only in light of the Trinity that we can see that the overarching God "over us", sent His Son to be "God for us". And in the person of the Holy Spirit, humanity has the prospect of "God within us", helping us to live the impossible life that God expects of the pinnacle of His creation. Humanity is to pour out our lives in service to others, as He Himself has done.