Step one: apologize.
Sometimes when people fight they say or do things that they do not mean, or that can be misconstrued, or that are hurtful. Thus, the first thing you should do is eat your pride and say you are sorry for fighting, and for anything you said or did that was not nice.

Step two: talk it out.
A lot of times in marriage the couple never really gets a chance to get to the root of the problem, so they smooth over the main problems, but leave scars under the glossing over. Instead of doing this, and leaving feelings that could erupt later, make sure you get your feelings out and help one another understand why a fight occurred in the first place. When you do this you learn how to avoid these problems in the future.

Step three: do something to reconnect.
A fight usually leads to some disconnecting. In an important relationship, like a marriage, to do something to not just end the fight, but repair the damage that was done and get back to the level you were at before. This can mean taking time just the two of you to do something you enjoy. It can be watching a movie together and snuggling. It can mean just going on a walk hand in hand. The point is, if you want things to be good again, you have to do something to remind yourself why you love each other.

Step four: don't repeat it.
One of the keys to a happy marriage is to make your make-ups real. If you are to make-up the right way you have to intend to never repeat the offense. If you know you will, then making up is not going to do any good. If you purposely repeat the offense, or are not going to try and keep yourself from doing it again, then your spouse will lose trust in you. So, if your spouse is upset that you did not help them clean the house, and you say sorry, then in the future you better help clean the house.

Step five: don't dwell on it.
Forgiveness is really important, you will never be able to make up if you can't let it go. So if you and your spouse make up, you better be prepared to let go of the hurt feelings. If you dwell on it, bring it up again in the future, or use it against them later, then making up with each other will be nothing more than a ritual and will lead to deeper problems later.