Every relationship is different, but every relationship has fights. Couples that stay together for the long haul usually figure out a way to make up and move on. If you don't want to just pretend the fight never happened, and just wait for the tension to blow over, read on for some advice on making up in an open and healthy way.
Look underneath the argument. There's a saying, "You're never fighting for the reason you think". It may look like you're fighting about money, sex, or something specific, but there's usually some vague feeling underneath that hasn't been expressed fully. It might stem from being hurt in previous relationships, or even childhood experiences. Identifying the root feeling can help with calming down. Some common feelings that many fights can be traced to are:
Inadequacy. You feel like you're just not good enough - you can't quite believe that someone like that would want someone like you - at least not for long.
Abandonment. You're worried that the person will leave you, if not literally, then perhaps by cheating on you, or becoming emotionally distant (this goes with inadequacy).
Being taken for granted. You feel unappreciated, perhaps used.
Communicate what's most true for you in one sentence. Learn How to Practice Nonviolent Communication. Letting your partner know "I feel scared when I see you talking to other girls" or "I feel angry I don't have the money to pay for this right now" allows you to get to the core issue and often helps him to understand where you're at without arguing about it.
Take responsibility. Did you snap at your mate? Are you trying to control the outcome? Is it easier to get what you want by manipulating the situation rather than simply asking directly? We all do these things to one degree or another. If you can find a way to own up to your part in the argument, without trying to blame or wrong yourself or your partner for it, it may just open up a whole new dialog. Be Humble. Sometimes if you can Apologize for something you did (even if you didn't "start" it) it can disarm your partner, and result in their apologizing as well. Something like, "Wait a minute. This is not where I wanted this to go, and I'm so sorry it has. I don't want us both to be so upset we can't even talk. Can we take a breather from the disagreement, collect ourselves and try again, only this time less angry?"
Let go of being "right". Wanting to be right in an argument is the surest way to keep it going. People will argue about who's right and who's wrong for years if they don't decide to do something else with their energy. It's a no-win situation and keeps you from truly connecting with your partner. There's an old saying: "Would you rather be right, or be happy?"
Let your partner learn in their own way, at their own pace. You can only control yourself, and your own pace of learning. If your partner isn't getting it, you can't force them to see what this issue might be about for them. You can only see what it's about for you. There's information in any argument for both of you, but it's impossible to make someone see things from your point of view. Either they do, or do not. And if they don't, you can either accept that, and learn to deal with it, or don't. But if you don't, the argument(s) will continue.
If you're holding out for an apology, and your partner isn't giving it, consider openly forgiving them anyway. This kind of acceptance, if you don't do it in a condescending way, might show your partner that you accept their imperfections, which can help them stop trying so hard to defend their flaws. Example: After succinctly expressing how you feel (as described earlier) say "I know you didn't mean to hurt my feelings by forgetting about our anniversary. I do still feel hurt, though, but I'm willing to trust that you didn't do it on purpose, and you'll try to remember next time. Ok?"
Appreciate your partner. The sooner you two can experience some form of joy and lightheartedness, the better. Successful relationships have a five to one ratio of appreciations to criticisms. Actions that create a genuine positive feeling will help to replenish the "emotional bank account" of your relationship. After an argument is a great time to re-balance your relationship by noticing and expressing lots of things that you really like about your partner and yourself, and the way you are together. If you're still feeling down about the whole thing, though, start with yourself: Cheer Up.
Make new agreements. If your argument has been a nasty one, you may want to make an agreement with your partner about the boundaries and terms of your relationship. For example "I agree not to call you nasty names." Or "I'd like for us to agree that we talk about what's going on without yelling at each other."
Learn from the argument. Is this argument much like others that you've had with others in the past? If you keep repeating the same arguments, it's because there's some learning that hasn't taken place yet, or some way in which you keep these issues going without realizing it. What might this issue that you've been arguing about have to teach you? If you face what you've been fighting about, you can often uncover the golden nugget of learning for yourself. If you aren't able to unearth a deeper meaning after reflection on both of your parts, you may have hit on a dealbreaker. If you're arguing about one issue over and over, and you cannot resolve it; and if one or both of you are unwilling to find a compromise (such as: one of you wants children, the other does not), then your relationship may not be a match made in heaven.
No one wins if, at the end of the day, you feel disconnected from each other.