JOEL - Actually the Mormons did not practice "polygamy"; the correct term is really "polygyny", which is the practice of a man having more than one wife. Therefore, you would never have the situation of a woman marrying more than one man.
The church started the practice because God told them to. It is an eternal principle but one that God has not commanded man to live at all times, except for when He determines that it is necessary. At the time the Church was first established it was necessary, in order to raise up a large number of believers in a short amount of time to firmly establish the Kingdom of God on earth. During this time it was a commandment that God wanted them to live. This is why there were some exhortations from the leaders that they must accept it in order to obtain the highest level of heaven. If they did not accept it, they were not obeying God's will. God no longer requires us to live it right now, so it is not required for us to live it to obtain the highest level of heaven, but we must accept it as a true doctrine of God.
Lamech was not the only one who had more than one wife. There was also Jacob(Genesis 31:17), Esau(Genesis 36:2,6), Abraham(Genesis 25:6), King David(2 Samuel 5:13), King Solomon(1 Kings 11:3), and Rehoboam(2 Chronicles 11:21), to mention a few more.
It was the Edmunds-Tucker Act of 1890 that supported the seizure of Church property because of the practice of plural marriage. After this it was clear to both God and the Church that plural marriage was leading toward the economic and political destruction of the Church. Therefore a short time later, a revelation was received by President Wilford Woodruff from God to withdraw the requirement for worthy males to take plural wives. He announced the Manifesto, formally stating his counsel to Latter-day Saints to abide by antibigamy laws (see D&C Official Declaration 1). The Manifesto ended the legal confrontation between the U.S. government and the Church. This action is in line with the Church's twelvth Articles of Faith which states:
"We believe in being subject to kings, presidents, rulers, and magistrates, in obeying, honoring, and sustaining the law."