Arguing is a part of life, and relationships. It can never be completely avoided, but there are ways of minimizing the arguing, and to avoid letting these small arguments escalate into full blown fights.
First off, open communication. You may think you and your partner talk about everything, but many times it's the little things that are overlooked that end up costing you the most in the long run. Most arguments start due to a lack of communication up front, or perhaps a miscommunication. For instance, many couples argue over money because one partner makes purchases without first consulting the other. This could be avoided by communication.
Be Honest about feelings and opinions. Often times we will pretend that something doesn't bother us, or that it's no big deal. If your partner does something you're unhappy about and you say nothing, it may be fine the first time. But if your partner has no idea that it bothers you, they will continue to do it over and over again. Eventually instead of calmly discussing the issue, you may just explode, leaving your partner bewildered because they had no idea they'd done wrong. Speaking up the first time, in a calm manner will reduce further tensions.
Look at the other person's point of view. Yes you want your feelings validated, but perhaps by trying to convince your partner that you are right, you're overlooking the fact that they have a side to the discussion as well. Stop for a minute and think about their feelings before continuing. If you put your feelings aside for the moment, and concentrate on theirs, they may be in a more receptive mood, and then you can discuss your own feelings.
Never let an argument get out of hand. Never resort to name calling, blackmail, or guilt trips to get your own way, this is only going to cause hurt feelings and resentment. If you're feeling over stressed from the argument, take a time out. Give yourselves 5 to 10 minutes to calm down and collect yourselves, apart from each other. Once you are calmer you may see things more clearly, so you can return to your original discussion.
Agree to disagree. Two different people will always have two different points of view. Neither of you will always be wrong and neither of you will always be right. Don't try to make your partner change to your way. Remember that you fell in love with their uniqueness and the more you try to make them like you, the less you will like them (believe it or not) and the more they will resent you. Just accept the fact that they have their own opinions, even though you may not share them. So long as they are not hurting themselves or anyone else, there's nothing wrong with the fact that they are different.
When your feeling stubborn and don't want to forgive your partner for whatever wrong they have done, ask yourself this; "What's more important to me, this person or this battle?" No, maybe you won't lose your partner over every battle, but is it worth taking that chance? Is it worth hurting their feelings and causing this tension? Many times we fight over small things, does it really make a big difference in the grand scheme of things? Learn to let smaller things go. Your relationship is more important, so pick your battles well.