It's hard to say exactly when polygamy started in Mormonism. There is no official record for what is generally felt to be the first plural marriage (by non-Mormon historians and Mormon historians alike. Please note that of course there are dissenters who do not accept this marriage). According to journals and notes however, Joseph Smith married Fanny Alger, aged 16, in Kirtland, Ohio some time in 1833. The next marriage has no official documentation either, to Lucinda Harris in 1838 in Far West, Missouri (already married to faithful saint, George Harris). Official church records list the first plural marriage to Prescindia Lathrop Huntington Buell on December 11, 1841, a woman already married to faithful saint Norman Buell.
1833 or 1841, those early polygamous marriages established Mormons as a minority community, a community that would be shunned, reviled, harassed and even threatened because of their family structure and sexual practices.* Rumors ran wild in the surrounding community, stories about how depraved the Mormons were, how they would break up families and destroy lives. Joseph Smith, aware of how polygamy was viewed not only by non members but by many of his own flock, practiced in secret (the formal announcement of what was known as the 'everlasting covenant' [see Doctrine & Covenants section 132] was not made until 1852) which meant that the women he and a small number of high church officials had married were unable to be recognized as family members, unable even to talk about the difficulties they faced. The thought of what those women, faithful women, went through in the years before they could be acknowledged is heartbreaking.
Still, there were many who stayed true (not all, but hey, it's a blog post and contrary to all evidence I don't want to write a novel!). It was a choice they had after all, a choice to accept this commandment. When an angel with a flaming sword told Joseph Smith that he had to marry multiple women to establish the principle of celestial marriage those women could have refused. But, caught between what society felt they should do and what they knew to be right, they chose polygamy.
Polygamy is more than a footnote in Mormon history. Joseph Smith spent considerable time and energy countering the rumors but Mormons, many of whom didn't know that polygamy was, in fact, being practiced by a few elders, continued to suffer from the fear-filled reactions of the surrounding community. Joseph Smith himself was arrested after he ordered the destruction of the Nauvoo Expositor, a newspaper that was going to publish information on the practice of polygamy (again, long story, historically accurate, available from acceptable Mormon sources). Following his arrest he ended up in a small jail, a house really, in Carthage, Illinois. A mob stormed the jail and Joseph and his brother Hyrum were killed - a martyr to the church, a martyr arguably to polygamy. Brigham Young was anointed the next prophet and president of the church and, under his leadership, polygamous marriages were continued and the practice was expanded. There were threats, discussions and multiple laws passed on the national level all to try to abolish the practice of polygamy - again, a practice that was not only accepted by the Mormons but was the law of God, the true nature of family, the celestial and holy order of things. Eventually, after unbelievable (and unconstitutional) pressure the church announced that they were abandoning the active practice of polygamy.
It's only the active, for now practice that's abandoned. Mormons still believe in the doctrine of polygamy in the next life. Dalin H. Oaks (for one) is sealed to his first wife and to his living wife and will, in the celestial kingdom, be with both women for all eternity. Bruce R. McConkie , in a non-scriptural book wrote: “the holy practice will commence again after the Second Coming and the ushering in of the millennium.” Doctrine & Covenants 132 remains scripture, meaning that doctrinally the Mormon church still puts themselves in a minority group, a group that has an unusual definition of family, a group that believes, at least on some level, in a marriage that is not one man and one woman.
If anyone could have empathy for the situation gay Americans find themselves I would think it would be the Mormons.
*Note: while modern Mormons often argue that Joseph Smith's many marriages were spiritual in nature the earlier church actually fought bitterly to prove that his plural wives were his physical as well as spiritual partners. Testimony was gathered by the church to counter claims by the splinter Reform LDS church founded by Emma Smith, Joseph's original wife, who contended that he had never practiced polygamy and any partnerships he formed were not consummated. There are numerous journal entries and testimonies that document that Joseph was indeed a fully practicing polygamist, testimonies that support his own contention that polygamy was a sacred doctrine introduced to 'build up the kingdom' - in other words to produce children.