Mormons are not taught to believe what traditional Christianity teaches about the Trinity. Mormons are taught that there are three entirely separate persons, not three persons in one. For Mormons, they are: God the Father (identified as 'Elohim' in the Bible), Jesus Christ, and the Holy Spirit.
They are not "one" in any fashion and there is no Trinity as defined in orthodox Christianity.
Christianity and the Trinity
According to orthodox Christianity, God is three persons in one: the Father, the Son, and the Holy Ghost. In some mysterious way, God is simultaneously three persons and one person — three completely separate persons who somehow share a single substance.
It's arguably not "strange" to reject such a bizarre concept, but what is arguably quite "strange" is rejecting a concept that lies at the heart of Christianity while also calling yourself a Christian. It's true that there was some debate about the validity of the Trinity and nature of Jesus in the earliest days of Christianity, but those debates were settled very early on.
Mormon Texts on the Trinity
Some of Joseph Smith's earliest writings appear to accept the traditional Christian doctrine of the Trinity, but that acceptance disappears over time. Eventually, he comes to repudiate the concept of the Trinity completely.
The book History of The Church of Jesus Christ of Latter-day Saints records Joseph Smith saying the following in a sermon on June 16, 1844:
"Many men say there is one God; the Father, the Son and the Holy Ghost are only one God! I say that is a strange God anyhow--three in one, and one in three! It is a curious organization. ...
All are to be crammed into one God, according to sectarianism. It would make the biggest God in all the world. He would be a wonderfully big God--he would be a giant or a monster."
This rejection of the traditional Christian doctrine of the Trinity is not limited to the earliest days of Mormonism; on the contrary, it continues today. Dr. Stephen Robinson writes in his book Are Mormons Christians?:
"If by “the doctrine of the Trinity” one means the doctrine formulated by the councils of Nicaea and Chalcedon and elaborated upon by subsequent theologians and councils—that God is three coequal persons in one substance and essence—then Latter-day Saints do not believe it."
Bruce McConkie writes:
"Three separate personages—Father, Son, and Holy Ghost— comprise the Godhead. As each of these persons is a God, it is evident, from this standpoint alone, that a plurality of Gods exists."
Critics of Mormonism often say that instead of orthodox Christian Trinitarianism, Mormons have adopted a tritheism — a type of polytheism consisting of three gods, as opposed to monotheism which is a theism of one god. This is because each member of the Mormon Godhead is not merely a separate person like in the Trinity, but also independent of each other, as is the case when you have separate gods.
There is no particular basis for tritheism in the Bible and at no point in the early development of Christianity was there ever any consideration given to this position. However, Mormons are also taught that the Bible has become corrupted and filled with errors. Joseph Smith was instructed by God to "restore" true Christianity through the divine revelations that Smith as receiving.
As Dr. Stephen Robinson explains:
"If the Father did not exist, neither the Son nor the Holy Ghost would be God, for their divinity comes through their relationship with the Father. ...
We believe this not because it is the clear teaching of the Bible but because it was the personal experience of the prophet Joseph Smith in his first vision and because the information is further clarified for us in modern revelation."
Denial of the doctrine of the Trinity and asserting that Jesus, the Holy Spirit, and God are all completely separate and fully independent is not something that Mormons typically talk about with non-Mormons. Rejection of such a center Christian doctrine would immediately cause many people to deny that Mormons are genuinely Christians, a debate Mormons would prefer to avoid. This is why prominent Mormons, especially politicians like Mitt Romney, keep quiet about such things when discussing their beliefs.