I would think the main rule in working through any problems would be for both people to respect and trust each other. With respect, you will be honest, supportive, and caring with your partner. With trust, you will be able to share any dreams, fears, or problems. It seems to me that if you can do these things, you can work out any problem you might encounter.
Talk to each other. It seems simple, but talking to each other helps everything out. When you get into an argument, don't wait to talk to him, there may be something wrong that he/she is not telling you.
Don't ever extend an issue longer then it needs to be. Humour can keep a relationship alive in a lot of situations :) Let eachother talk, if you didn't understand each other at least a little you wouldn't be together in the first place! Sometimes a lil walk away from one another is best to cool down, and maybe re approach the problem in a different more constructive way. And always treat your partner as if you would treat your friend. Never lose sight of what you two have together and if it is a strong bond, you will be fine. If you split the ups and downs and there are more downs then ups? Maybe its time to move on and find something better!