How can a Christian have a romantic relationship with a non-Christian? How do you deal with someone who doesn’t believe in God if you have different life views?

The best thing is if you are a Christian and the other person is not a Christian to avoid getting romantically involved. From a biblical perspective we have many verses warning of mixed marriages with people who are committed to other gods.

Do not be unequally yoked with unbelievers. For what partnership has righteousness with lawlessness? Or what fellowship has light with darkness? What accord has Christ with Belial? Or what portion does a believer share with an unbeliever? What agreement has the temple of God with idols? For we are the temple of the living God; as God said, “I will make my dwelling among them and walk among them, and I will be their God, and they shall be my people. Therefore go out from their midst, and be separate from them, says the Lord, and touch no unclean thing; then I will welcome you, and I will be a father to you, and you shall be sons and daughters to me, says the Lord Almighty.”
(2Corinthians 6:14-18)

This is also true sociologically.

Statistics show that 37 percent of Americans have a spouse of a different faith.
Statistics also show that couples in interfaith marriages are “three times more likely to be divorced or separated than those who were in same-religion marriages.”

So to the degree that we make a choice about which people we date and open our heart to it is wiser for us to not become romantically involved with someone of a different faith. This is a moral command for Christians who are to only date and become married to people who also hold to a Christian faith.

However, if a Christian is already married to a person who is not a Christian they should stay married. God’s will is for you to stay in the marriage as long as your spouse wants to be in the relationship. God may use you in that case to bring the family to the faith in time.

If any woman has a husband who is an unbeliever, and he consents to live with her, she should not divorce him. For the unbelieving husband is made holy because of his wife, and the unbelieving wife is made holy because of her husband. Otherwise your children would be unclean, but as it is, they are holy.
(1Corinthians 7:13-14)

Now if you are already in a romantic relationship with a person of another faith or “no faith” then how can you handle this situation? Admit that this is not a wise choice and end the relationship since the spiritual and emotional risk is high and any hope of a good outcome small. So gently end the relationship and strive to only become involved with people who are Christians.
Now outside of marriage and romantic relationships the way we must deal with people who are of different faiths and life views is that we need to love them as our neighbor, respect as made in the image of God, love them as our enemies in regard to the truth of the gospel, and seek to find common ground with them where we can. We must understand that adults have the right to disagree and so while we may disagree with what they think and do, we can still respect them.

Unbelievers are still able to be influenced by the common grace of God and may even have insights for us at times. Abraham the prophet of God is rebuked by the pagan Pharaoh when he has lived by fear instead of faith (Genesis 12:19). So unbelievers may speak the truth and have useful insights about many aspects of life because God is still their creator and has grace upon them.

The believer should hope that perhaps a divine opportunity will open with those that do not have faith and they may through the testimony in word and deed of the believer come to faith. So we should love unbelievers and respect them.

However, Christians should not get romantically involved with people of other world views if this can be avoided.

http://www.washingtonpost.com/wp-dyn/content/article/2010/06/04/AR2010060402011.html