While the Father, Son, and Holy Ghost are separate beings, they function as one God, or Godhead, to oversee, bless, and save the human family. There is no competition between Them. They are "one", and share a perfect love and unity. Moreover, They desire that we too share a relationship of love. See "That They May Be One As We Are One".
To avoid confusion, I should clarify and separate two different concepts here. There are two different kinds of plurality: the plurality within the Godhead (only three) and the plurality that arises from the fact that exalted children of God can be called gods. Whether we're talking about a plurality of Gods within the Godhead (Father, Son, and Holy Ghost), or a plurality of gods (ie: all the "sons of God"), it doesn't change the fact that there is only one true source of worship, love, power, light, and glory in the universe--God the Eternal Father, His Son, Jesus Christ, and the Holy Ghost.
Elder M. Russell Ballard touched on both kinds of "plurality" and their accompanying confusion years ago in a talk entitled, "Building Bridges of Understanding":
[An] area of misunderstanding among some of our friends in Christianity is that they refer to us as “polytheists,” meaning that we believe in a plurality of Gods. Much misunderstanding would be avoided if they understood that we worship only one Godhead, consisting of God the Father, God the Son, and God the Holy Ghost. We believe that the biblical record teaches that God the Father, Jesus Christ, and the Holy Ghost are separate persons. When the Savior was baptized, the Father spoke His approval from heaven, and the Holy Ghost was witnessed to be present by the sign of a dove (see Matt. 3:16–17). Likewise the Bible records the prayers of Jesus Christ to our Father in Heaven, a separate being (see John 17:3). We believe this doctrine is taught in the Bible despite what the creeds of other Christian denominations may teach. Such creeds were created hundreds of years after Christ’s mortal ministry through the processes of debate and compromise, often at the expense of biblical truths. The falling away from the teachings of Jesus Christ resulted in the Apostasy, which made the restoration of the gospel essential. This is a subject to be studied by all; the various Christian creeds were born through church councils and other efforts to define the true nature of God and His Son, Jesus Christ. Through revelations to modern prophets, we now know God the Father, God the Son, and God the Holy Ghost and our true relationship to each one of them.
There is another related dimension of the scriptures that causes discomfort for many traditional Christians regarding this whole matter. We believe our Father in Heaven has promised His faithful sons and daughters “all things”—even that those worthy of exaltation in the celestial kingdom will be as “gods, even the sons of God” and that “these shall dwell in the presence of God and His Christ forever and ever” (see D&C 76:55, 58, 62). Although we do not know the full detail of these promises or what is fully meant by being “gods, even the sons of God,” we do accept these promises as revealed doctrine. Yet notwithstanding these promises, we say that for us there is indeed no other object of worship than God the Father, the Son, and the Holy Ghost.
Now, in fairness to credal Christians, the doctrine of the Trinity also recognizes that the Father, Son, and Holy Ghost are separate persons (that is, that the Father is not the Son and the Son is not the Father), but it holds that these divine persons mysteriously share the same ousia, substance, or being. Latter-day Saints recognize that there is more than one way to worship the Father, Son, and Holy Spirit as "one God" than simply numerically as one ousia. These three divine persons are one in purpose, love, unity, and just about every other way except physically. Thus, Mormons also believe in "one God", even though we know each has their own being/ousia. (ie: D&C 20:28: "Which Father, Son, and Holy Ghost are one God, infinite and eternal, without end."). Therefore, notwithstanding this separateness of being, or plurality of Gods within the Godhead, because they are "one", there is no polytheism.
On the most misunderstood point of a plurality of gods in reference to LDS belief in deification, people need to understand that "becoming a god" is not the equivalent of setting up independently from God, replacing or displacing God, or competing with God. Deification involves becoming the sons of God, and this is done only in and through a loving relationship with God, and becoming one with the Father and the Son as Christ prayed we would in John 17. Stephen Robinson explains in his book "Are Mormons Christians?":
Some believe that certain LDS doctrines are so bizarre, so totally foreign to biblical or historical Christianity, that they simply cannot be tolerated. In terms of the LDS doctrines most often criticized on these grounds, however –the doctrine of deification and its corollary, the plurality of gods–this claim does not hold up to historical scrutiny. Early Christian saints and theologians, later Greek Orthodoxy, modern Protestant evangelists, and even C. S. Lewis have all professed their belief in a doctrine of deification. The scriptures themselves talk of many "gods" and use the term god in a limited sense for beings other than the Father, the Son, or the Holy Ghost. If this language is to be tolerated in scripture and in ancient and modern orthodox Christians without cries of "polytheism!" then it must be similarly tolerated in the Latter-day Saints.
If scripture can use the term gods for nonultimate beings, if the early Church could, if Christ himself could, then Latter-day Saints cannot conceivably be accused of being outside the Christian tradition for using the same term in the same way.
I don't need to argue whether the doctrine is true, although I certainly believe it is. I am only arguing that other Christians of unimpeachable orthodoxy have believed in deification long before the Latter-day Saints came along, and that it has been accepted and tolerated in them as part of their genuine Christianity. Fair play demands the same treatment for the Latter-day Saints.