Arguments are common in all relationships, but the most important thing is how you move past it.
All couples fight, argue, debate, discuss, or whatever word you want to assign to it. It comes down to two different people seeing things in ways that can be marginally to vastly different, depending on the subject and the couple.
The point is that they disagree about something that needs to be sorted out to move past it. What's important with this is how you move past it. Do you fight constructively or is it more like slinging mud?
1. Choose your words wisely.
One of the first rules in fighting with your partner is to remember the importance of choosing your words wisely. Keep in mind that once those words leave your mouth and your partner hears them, they can never be taken back.
This isn't the time to take something you know really bothers your partner on a personal level and turn it back onto him or her. It will just hurt that much deeper and may drive a permanent wedge between the two of you.
Unkind and hurtful words do more damage at times than a physical punch might have done. Obviously, hitting someone isn't right, but that's just to show how painful some words can be. Screaming hurtful words at your partner would not be considered constructive fighting; it's mudslinging, pure and simple. Mudslinging isn't going to get you anywhere except, possibly, single.
2. Fight constructively.
On the other hand, constructive fighting is useful and can actually solve important issues between couples. This type of fighting is usually conducted passionately, but without a lot of anger involved. Of course, that can change in a heartbeat depending on the subject and whether or not one or both partners are being unreasonable.
For instance, if it's about your partner insisting you spend every holiday with his or her family and you'd like to get some equal time with your own family, that can turn into one of those unreasonable fights. As a side note to this one, your partner is a very selfish and self-centered person, and you should have noticed this before you became a true couple.
Sitting down and talking about something is mature and offers faster, more effective solutions to a problem than screaming and yelling at each other. Seriously, how will you even hear what the other one is saying over all of that screaming?
3. Know how to deal with your anger.
If you MUST get some loudness out of your system, go ahead; just don't ruin the following calm where the two of you should reasonably discuss whatever the issue is and reach some workable resolution to it.
Anger is a very common emotion in any relationship. The range of anger is the one aspect that differs. Some people fly off the handle at the drop of a hat, while others are quietly angry. When a situation arises, if there's a lot of anger involved, the two of you need to separate for a few minutes until both of you have calmed down enough to have a conversation without all the mudslinging. Then, you can find the needed middle ground without destroying your relationship in the process.