The short answer to this is: No. Members of The Church of Jesus Christ of Latter-Day Saints are not in any way instructed to or encouraged to practice polygamy.
No matter what you have seen on television or what you've heard about "Mormons," it's not true that the mainstream LDS church promotes the practice of polygamy as part of its religion. In fact, any member of the LDS church who is found by church leaders to be practicing polygamy will be immediately excommunicated. The LDS church is so eager to make it clear that it does not practice polygamy, that even children of polygamists cannot be baptized into the mainstream church unless and until they are adults and they disavow the practice of polygamy.
That said, the long answer to the question above is: it depends on what you mean by "Mormon" and by "polygamy." There are many off-shoots of the mainstream LDS church which do, in fact, continue to practice various forms of polygamy, which was originally practiced during the mid to late 1800s by the early Mormon pioneers who came to Utah after being persecuted and driven out by mobs in Nauvoo, Illinois after being driven out by other settlements in the Eastern United States. The LDS church has recently admitted that polygamy was first practiced secretly by Joseph Smith in Nauvoo, before Brigham Young and the pioneers came to Utah, where "the Principle" was practiced widely and openly for some years.
Why did Mormons stop practicing polygamy? In 1890, after the United States government had made it increasingly difficult for polygamous members of the church and finally with the Edmunds-Tucker Act allowed the confiscation of all church property, President Wilford Woodruff issued a revelation from God called "The Manifesto" that said that it was time to stop practicing polygamy. This was difficult, of course, for those Mormons who were already in polygamous marriages, and there is certainly evidence that not everyone even in the higher echelons of the LDS church followed the Manifesto's edict. Some Mormons who wished to continue to practice polygamy fled to Mexico or Canada. Others divorced or separated, but continued to financially support formerly polygamous wives and children. Some men continued to cohabit with multiple wives and to father children until the second Manifesto in 1904 by Joseph F. Smith, when polygamy was banned even in Mexico for the LDS.
Some LDS continued to talk about polygamy as something that was an eternal law based on D&C 132 , but that would not be practiced until it became legal again at some time in the future. Wilford Woodruff himself had been known to say that polygamy would become legal again in the future. Other LDS church members believed for some time that polygamy was a "celestial law" that would be practiced in heaven, and was a law that God Himself practiced. But in the latter part of the twentieth century and continuing to the present, the mainstream LDS church has become increasingly strident in its support of one-man/one-woman marriage. It is difficult to imagine the mainstream LDS church today sanctioning the practice of polygamy once more among its members.
As for the offshoots of the Mormon church which continue to practice polygamy, it is important to make distinctions between them. Some call these groups "fundamentalist Mormons," because they think of themselves as practicing an older and truer form of Mormonism, but none of them practice polygamy as it was taught by Joseph Smith or Brigham Young. While the mainstream LDS church has over 16 million members and is one of the fastest growing churches in the world, with large groups outside of the United States, in Latin America in particular, the polygamous and fundamentalist off-shoots of Mormonism seem to grow only by a prodigious birthrate and do not proselytize throughout the world -- indeed seem to have no interest in doing so.
The largest fundamentalist Mormon group is the Fundamentalist Church of Jesus Christ of Latter-Day Saints (FLDS, about 8,000 people), which has become well-known because of the conviction of its leader, Warren Jeffs, for crimes including rape. It is important to note that the practices of marrying closely related family members, which has led to widespread problems of incestuous birth defects is not part of the original Mormon practice of polygamy as promoted by Brigham Young. Nor is the marriage of 12 year-old girls who have barely had a chance to have an education part of historical Mormon polygamy. Underage marriages may have happened, but they were a rarity.
Other, smaller polygamist "Mormon" groups include the Apostolic United Brethren (AUB, less than 1,000 people), the TLC (True and Living Church of Christ), the Centennial Park group (in Arizona), the Righteous Branch led by Rulon Allred, and the Latter-Day Church of Christ led by the Kingston clan. These other groups largely do not practice under-age marriage and seem to have less cult-like tendencies in allowing people to move in and out of plural marriages depending on their own choices, rather than threats and monetary lures. But the solemn practice of marrying in Mormon temples for eternity, as was done in the 1800s through most of Utah under the direction of the prophets and apostles of the LDS church, is no longer possible for these polygamists, no matter what their claims are to living the "true" principles of historical Mormonism.
There are some who claim that polygamy continues to be taught in mainstream LDS churches because D&C 132 is still part of LDS scripture and there has been no significant change in its wording about the practice of "celestial marriage." It is also true that LDS men whose wives have died can be sealed for time and all eternity to a second or even third wife within LDS temples, while women whose husbands have died can marry for "time only" a second husband in the temple. Most of the LDS don't spend a lot of time worrying about this, and assume that "God will work it out." The church has begun to allow descendants to seal women who have died to more than one husband after the death of the woman in question, confirming the idea that both men and women will be able to choose their eternal spouses in the after-life.
What is my personal opinion on the matter of polygamy? As a practicing Mormon, I have not heard polygamy mentioned in church in many years, except when discussing the early leaders of the church, and even then, it is often with embarrassment and eagerness to move onto something else. Does that mean that the church is trying to hide the truth? I suspect it is more that no one is willing to say that the early church leaders were wrong about polygamy because it puts in doubt other truth claims about the church, but at the same time, no one wants to talk about polygamy, either.
While the legacy of Mormon polygamy in abusive sects like the FLDS is troubling to me personally, the modern practice of polygamy among the FLDS is quite distinct from the practice within the mainstream LDS during the late 1800s. As for whether or not I believe polygamy will be the law of heaven, well, I will try to send back some information when I get back to the other side. Until then, I'm content to be assured that my husband and my children are my celestial family without any of us needing more covenants than the ones we have vowed to each other.