First, what does the Catechism of the Catholic Church (CCC) has to say about this?

So the Church is very clear that part of our duty as members of society is to participate in our country's rule through use of our vote. However, as the U.S. Conference of Catholic Bishops (USCCB) also says: 

How does the Church help us to form our conscience well in regard to voting? While not specifically endorsing particular parties or candidates, there are guiding principles that are put forward. It is the obligation of Catholics to keep this in mind as they research a particular political platform and candidate(s) in the process of casting a vote - a process that should begin before entering the polling place.

Intrinsically evil actions are those that fundamentally conflict with the moral law and can never be performed under any circumstances. It is a serious sin to deliberately endorse or promote any of these actions, and no person who really wants to advance the common good will support any action contrary to the non-negotiable principles involved in these issues:

Abortion. In his encyclical Evangelium Vitae (EV, "The Gospel of Life"), Pope St. John Paul II taught that, regarding a law permitting abortions, it is "never licit to obey it, or to take part in a propaganda campaign in favor of such a law, or to vote for it" (EV 73). Abortion is the intentional and direct killing of an innocent human being, and therefore it is a form of homicide. The unborn child is always an innocent party, and no law may permit the taking of his life. Even when a child is conceived through rape or incest, the fault is not the child's, who should not suffer death for others' sins. Another sub-set issue within this subject area that is non-negotiable pertains to Human Reproductive Technologies, which includes the Church’s position against Contraception, In-Vitro Fertilization and Sterilization.

Euthanasia. Often disguised by the name "mercy killing;' euthanasia is also a form of homicide. No person has a right to take his own life, and no one has the right to take the life of any innocent person. In euthanasia, the ill or elderly are killed, by action or omission, out of a misplaced sense of compassion, but true compassion cannot include intentionally doing something intrinsically evil to another person (cf. EV 73).

Embryonic Stem Cell Research. Human embryos are human beings. "Respect for the dignity of the human being excludes all experimental manipulation or exploitation of the human embryo" (Congregation for the Doctrine of the Faith, Instruction on Respect for Human Life in Its Origin - RHL, 4b). Recent scientific advances show that medical treatments that researchers hope to develop from experimentation on embryonic stem cells can often be developed by using adult stem cells instead. Adult stem cells can be obtained without doing harm to the adults from whom they come. Thus there is no valid medical argument in favor of using embryonic stem cells. And even if there were benefits to be had from such experiments, they would not justify destroying innocent embryonic humans.

Human Cloning. "Attempts ... for obtaining a human being without any connection with sexuality through ‘twin fission,’ cloning, or parthenogenesis are to be considered contrary to the moral law, since they are in opposition to the dignity both of human procreation and of the conjugal union" (RHL 1:6). Human cloning also involves abortion because the "rejected" or "unsuccessful" embryonic clones are destroyed, yet each clone is a human being.

Homosexual "Marriage". True marriage is the union of one man and one woman. Legal recognition of any other union as "marriage" undermines true marriage, and legal recognition of homosexual unions actually does homosexual persons a disfavor by encouraging them to persist in what is an objectively immoral arrangement. "When legislation in favor of the recognition of homosexual unions is proposed for the first time in a legislative assembly, the Catholic lawmaker has a moral duty to express his opposition clearly and publicly and to vote against it. To vote in favor of a law so harmful to the common good is gravely immoral" (Congregation for the Doctrine of the Faith, Considerations Regarding Proposals to Give Legal Recognition to Unions Between Homosexual Persons, 10).

In today's society these beliefs are widely opposed, and it may be difficult to find candidates that are in agreement with all (or, indeed, many) of them. However, we are still to make a prudential judgement before casting our vote. We are certainly cautioned not to vote for someone specifically because they support one or more of these issues, but we may need to weigh the moral implications in light of other initiatives they support. 

Our nation is blessed to be structured in such a way that we can place people who best represent that nation's views in positions of power, and our vote is participation in that power - let's use it to bring our nation back to a Culture of Life!