1. Communication is vital, now more than ever.
You have different ideas of "Common Sense". You have different methods of talking through things, and likely different ways of addressing situations. In spite of the functional dissonances, as long as both people communicate regularly, it shouldn't be too hard.
2. Every moment has a lesson attached.
Whether it be about the other's culture, about how they think, about where exactly they came from, or what they've been through. There's always something to pick up. Most of the time, it will be small things, but they add up. Every now and then, you might learn something which would play a central role in where you go from there. Keep your eyes and ears open.
3. Try and find common ground, but cherish your differences
To quote Thinking Fast and Slow, "We are sufficiently similar to understand each other easily and sufficiently different to surprise each other." This rings especially true in this kind of relationship.
4. When working together, work very closely.
Whether it's on work needing to be done, or a simple game, every moment can be an excuse to exercise cooperation skills. It's important for friends, but even more so for significant others.
5. Make an attempt to learn the language.
If one person speaks a language unknown to the other, that's a perfect opportunity. Nelson Mandela once said, "Talk to a man in a language he knows, that goes to his head. Talk to a man in his language, that goes to his heart." Heart-to-heart talks are one thing when it's a couple, but to do it in one or the others' native language is another level of depth, especially when the two do not share a primary language. It's a touching gesture.
6. You don't have to like absolutely everything.
Cultural barriers will cause rough moments. There will be moments of disagreement. You will genuinely dislike certain parts of the other person. But that's okay. If you're looking for a person who loves every part of you, and you love every part of them, just know that the person you're looking for doesn't exist. The important thing is to make sure that the things you don't like interfere with what you do like.
7. If there's an underlying problem, deal with it head on.
If you let any problem linger, it constantly gets worse. Whether it's a small disagreement or a recurring event, deal with it immediately.
At the end of the day, it isn't terribly different from any other relationship. It's all about commitment to one another. As long as you're willing to share a few burdens back and forth and willing to work with one another, it should be smooth sailing.
