How should Catholics vote?

Easy, based on the teachings of the Catholic Church, that's how. The statement by the USCCB is pretty clear. We should be involved in our country's political life. Voting is not the only way. When we vote, we should be informed by Catholic moral teaching. We cannot put party loyalties or loyalties to a politician ahead of Catholic teaching. We sure cannot vote for individuals or measures in order to advance something that is deemed an intrinsic moral evil by the Church. You cannot vote for someone who supports moral evils simply because. If you do vote for one person who advocates a grave moral evil, it had better damn well be because you are hoping it will cancel out an even greater moral evil. If you can't bring yourself to vote for any candidate, you can take the extraordinary step of just not voting (notice the emphasis on extraordinary step - that suggests that voting is the assumed approach to preforming our civic duties). If you feel you have no choice between two candidates or parties, you can - as long as you are being honest with God, who of course knows - vote for the one who is least morally offensive if it is to prevent greater moral evils of the other party or advance greater moral goods:

When all candidates hold a position in favor of an intrinsic evil, the conscientious voter faces a dilemma. The voter may decide to take the extraordinary step of not voting for any candidate or, after careful deliberation,may decide to vote for the candidate deemed less likely to advance such a morally flawed position and more likely to pursue other authentic human goods.

Ultimately, how you vote is between you and God.

That's it. The basic ideas is that you should vote. As Americans, we should sometimes remember just how precious this thing called freedom is. I notice sometimes we tend to take it lightly. We assume that, no matter what happens, things will be the same. If America slides down the scale of world powers, or some other country emerges, it will all be the same. Despite our railing against American Exceptionalism, everyone seems to think that America as it is will be around forever. It won't. Enjoy the freedom while we can.

Also, don't let folks tell you that voting a certain way, or even voting at all, is a sure path toward damnation. In the 2008 election, I was shocked at how many Catholic apologists tried to insinuate that only dolts and sinners wouldn't vote their way, or even would vote at all. There was actually attempts by some notables to suggest that the very act of voting puts one's soul in jeopardy. Since Catholics have the benefit of an actual, physical teaching authority, they should listen to them. The Bishops have made it clear we should take part in the political process, we should do it as Catholics first, we can never vote to promote, or even support someone who does promote, intrinsic evils. And if there is no other choice, we can abstain, or try to take the path to eliminate the worst evil or promote the best good in the most efficient way. All of it being, of course, between the voter and the Maker.

Pretty simple, huh. Don't let anyone tell you otherwise. If they are trying to suggest they vote the way Jesus would, and only idiots or sinners could disagree, then rest assured if you smell a rat, you're right.

It must be noted also that a well-formed Christian conscience does not permit one to vote for a political program or an individual law which contradicts the fundamental contents of faith and morals. The Christian faith is an integral unity, and thus it is incoherent to isolate some particular element to the detriment of the whole of Catholic doctrine. A political commitment to a single isolated aspect of the Church’s social doctrine does not exhaust one’s responsibility towards the common good. (Doctrinal Note on Some Questions Regarding the Participation of Catholics in Political Life, no. 4)