Is the concept of God in Christianity (the Trinity) three Gods or One? I don't understand the concept of God in Christianity. Based on what I do know, there is God, the Son of God and the Holy Spirit -- doesn't this add up to 3 Gods?

In Christianity, is there there One (True God) or are there three gods? If there are three gods, what is the role of each one? And who was the original God? Who is the father to the "Son of God"?
Firstly, the Trinity is not Tritheism. This is the classic argument of the Muslim against Christianity, but it is not valid. It is not valid, because the formulation of the Trinity specifically states that God is one being who exists in three persons. 

The Athansian Creed (a very ancient creed dating to the fourth or fifth century predating the Orthodox / Catholic / Protestant schims and accepted by at least 97% of all Christians) in particular states:


  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.


The problem is not in the formulation, but rather in attempts to make an analogy to explain it. There are great light-hearted attempts at analogy, but each suffers from a defect of some kind. No analogy is possible, because there is no terrestrial equivalent that properly holds the tension of the fact that three people with distinct energies, capable of perfectly relating to each other, are thus so close as to be One being. Every Trinitarian heresy comes out of an attempt to force such an analogy. 


Tritheism in particular was endemic to those areas of Christianity that are now under Muslim control. Tritheism emphasizes the distinct personalities to the detriment of their unity. The Father, Son, and Holy Spirit are indeed so close as to be one, in the same way a Muslim would agree that a man and wife are one flesh. Sometimes the analogy of the egg (shell, yolk, and white) is used to describe this relationship, but really it doesn't convey the simultaneous distinction and sameness of personality.
Modalism, on the other hand, makes the opposite mistake. It says that the Three manifestations of God are just different aspects of the same entity. (For example, some will say water is ice, fluid, and steam, or a man is father and husband)  That, however, precludes the ability of, say, God the Father to exalt God the Son (Phillipians 2:9). 


That being said, the primary means of differentiating the three persons of the Trinity is by their observed actions in history:


God the Father is the primary actor in the history of Israel and the Old Testament. He is identified by his love, jealousy, and protection of his people. For his own glory, he rescued his people from Egypt, and showed himself powerful on behalf of those whose hearts were perfect toward him. 
God the Son is known primarily through his actions as the incarnated Jesus of Nazereth.  According to John, he existed from the beginning of Creation, and he made all things. By him there is nothing made that was made. He chose to temporarily give up the rights of godhood in order to become a man. Being found in human likeness, he was obedient unto death, even the death of a cross.
God the Holy Spirit is known primarily through his actions in the church.  God the Son sent Him to dwell amongst his people, and was most visibly manifest at Pentecost. He is the source of the gifts manifest amongst Christians and is present in His church.


None of these actors acts out of accord with any of the others, and they all have the same character and purpose. They do have unique wills, but willingly subordinate them to each other in perfect harmony.

The truth is there is no analogy because there is no terrestrial equivalent. That said, both Muslims and Christians would agree that God is so far above humans that his Nature could be incomprehensible to his creation. That God is both Three and One is the core tenet of our understanding of who God is. In no way do Christians believe there is more than one God, but how we express that remains a paradox we cannot or have not resolved since his nature was revealed.