Twelfth Article of Faith

12 We believe in being subject to kings, presidents, rulers, and magistrates, in obeying, honoring, and sustaining the law.

We should obey the laws of the land wherever we live.  When possible we should vote for government officials and for laws that best coincide with God's laws and morals.

When Joseph Smith wrote this Article of Faith, the Latter Day Saints were not treated very well by the government.  The Saints were persecuted and forced to leave places they tried to settle.  Governor Boggs of Missouri issued an extermination order forcing the Mormons out of Missouri. Even after settling in the Utah Territory, President Buchanan sent Johnston's Army to Salt Lake City to confront the Mormons. So, I imagine this might have been difficult for the Saints to obey, honor and sustain the law In the early days of the Church. Nevertheless this is doctrine that was followed by early church leaders.  When asked by President James K. Polk for "a few hundred Mormon's" to join the US military to fight in The Mexican-American war, Brigham Young encouraged volunteers.  The Mormon Battalion was formed.

Today we are facing challenges with laws of the land that do not coincide with God's laws.  Some examples that come to mind are same-sex marriage, assisted suicide, and legalized marijuana. All three of these are legal in my state of residence.

Elder Oaks explains that man's laws do not change God's laws:

"Our twelfth article of faith states our belief in being subject to civil authority and “in obeying, honoring, and sustaining the law.” But man’s laws cannot make moral what God has declared immoral. Commitment to our highest priority—to love and serve God—requires that we look to His law for our standard of behavior. For example, we remain under divine command not to commit adultery or fornication even when those acts are no longer crimes under the laws of the states or countries where we reside. Similarly, laws legalizing so-called “same-sex marriage” do not change God’s law of marriage or His commandments and our standards concerning it. We remain under covenant to love God and keep His commandments and to refrain from serving other gods and priorities—even those becoming popular in our particular time and place."  -- Elder Dallin H. Oaks, "No Other Gods", October 2013 General Conference

Even though we believe in obeying, honoring, and sustaining the law -- man's laws, civil laws, laws of the land, will never change the morality of God's laws.  God's laws will always trump those created by man.