All of the other answers so far have presented the Trinity as a belief in one God. And this, of course, is what all Christian churches and denominations that hold to the doctrine of the Trinity say.
In the interest of balance, I will offer a countervailing view based on the Athanasian Creed and the theology of Emanuel Swedenborg (1688-1772).
The situation is more complex than simply saying that the Trinity is one God, as evidenced by this statement in the Athanasian Creed, which is accepted as authoritative by the vast bulk of Christians and Christian denominations:
For like as we are compelled by the Christian verity; to acknowledge every Person by himself to be God and Lord; So are we forbidden by the catholic religion; to say, There are three Gods, or three Lords. (Source: Athanasian Creed, from Wikipedia)
This statement perfectly encapsulates the fundamental contradiction in the doctrine of the Trinity, and the reason why every Christian theologian who expounds on it admits that it is a mystery that cannot be understood by the human mind, but that must nevertheless be believed.
The practical reality is that in thinking of Father, Son, and Holy Spirit each as distinct "persons" of God, the mind of the believer inevitably thinks of them as three different beings. This is tantamount to thinking of three gods, no matter how vigorously the believer says "one God" with the lips. Each person of God is given a distinct role, and they are conceptualized as interacting with one another as distinct personalities.
To illustrate this picture of three gods in the minds of those who believe in the Trinity, in Christian artwork the Trinity is commonly pictured as three distinct beings. In Western Christianity, most commonly the Father is pictured as an old bearded man, the Son as a young bearded man (often on the cross or associated with the cross), and the Holy Spirit as a dove. For example:
Holy Trinity, fresco by Luca Rossetti da Orta
In Eastern Christianity, artwork depicting the Trinity often simply has three human figures. For example:
Trinity (Andrei Rublev)
Clearly, though the lips are saying "one," the mind is thinking "three." But as the Athanasian Creed says, the church forbids the faithful from saying "There are three Gods." Therefore faithful Christian trinitarians will always say, "There is one God."
Here is how Emanuel Swedenborg articulates this contradiction between what the mind is thinking and what the lips are saying, based on the Athanasian Creed. This is from Swedenborg's True Christianity, #172:
At a conceptual level, the idea of a trinity of divine persons from eternity (meaning before the world was created) is a trinity of gods. This idea is impossible to wipe out just by orally confessing one God. The following words in the Athanasian Creed make it very obvious that a trinity of divine persons from eternity is a trinity of gods:
The Father is one person, the Son another, and the Holy Spirit another. The Father is God and Lord, the Son is God and Lord, and the Holy Spirit is God and Lord. Nevertheless there are not three gods and lords; there is one God and Lord. Just as Christian truth compels us to confess each person individually as God and Lord, so the catholic religion forbids us to say three gods or three lords.
This creed has been accepted by the entire Christian church as ecumenical or universal. Today everything known and acknowledged about God comes from it. Those who took part in the Council of Nicaea that gave birth to this posthumous child called the Athanasian Creed had no other concept of the Trinity except a trinity of gods, as any can see who merely keep their eyes open as they read it. Since then they have not been the only people thinking in terms of a trinity of gods; the Christian world thinks in terms of no other Trinity because its whole concept of God comes from that creed and everyone now lives in a faith based on those words.
I submit it as a challenge to everyone—both laity and clergy, laureled professors and doctors as well as consecrated bishops and archbishops, even cardinals robed in scarlet and in fact the Roman pope himself—that the Christian world nowadays thinks of no other Trinity except a trinity of gods. You should all examine yourselves and then speak on the basis of the images in your mind.
The words of this creed—the universally accepted teaching about God—make it as clear and obvious as water in a crystal bowl. For example, the creed says that there are three persons, each of whom is God and Lord. It also says that because of Christian truth, people ought to confess or acknowledge that each person is individually God and Lord, but that the catholic or Christian religion or faith forbids us to say three gods or lords. This would mean that truth and religion, or truth and faith, are not the same thing; they are at odds with each other.
The writers of the creed added the point that there is one God and Lord, not three gods and lords, so that they would not be exposed to ridicule before the whole world. Who would not laugh at three gods? On the other hand, though, anyone can see the contradiction in the phrase they added.
Certainly, due to the insistence of the Bible and the church that there is one God, Christians who believe in the Trinity will always and emphatically say that there is one God.
But no matter how many times this is said, the concept in the minds of those who believe in the Trinity is of three divine beings. This amounts to thinking of God as three gods, regardless of any abstract metaphysical statements about their being "one in essence," and regardless of the continually repeated statement that the three are one God.
All of this is why Jews, Muslims, and other strict monotheists commonly consider Christians to be tritheists rather than monotheists.