Realize that fights can be constructive ways to resolve issues and discuss your differences. After the argument and the apologies, take the time to analyze what you fought about and find ways to compromise and solve the problem together.
Think about what you say before you say it. Although you're in the heat of the moment, try not to make accusations or sling insults that your partner won't be able to forget. Conversely, try not to take what your significant other says too personally when she says it in anger.
Stay focused on the topic that started the argument in the first place. If you simply use the fight as an excuse to vent everything that's been bothering you about your significant other, you might never resolve the core issues.
Take a break in the middle of the fight to cool down and evaluate the points you're trying to make. If the argument has escalated, you may both be too defensive to truly listen to one another. However, agree that you'll continue when you come back even if you feel better. The issue may resurface if you just make up and fail to resolve it.
Use the opportunity to learn more about your significant other. Re-evaluate your relationship if he shows signs of physical or psychological abusiveness, proves to be passive-aggressive, calls you names or belittles you repeatedly during the argument.