Before you freak out, realize that it's absolutely normal for couples to have disagreements. It doesn't matter how many "cutest couple ever" awards the two of you have displayed on your mantle, you are in a human relationship and human relationships always run into disagreements.
But just because relationship issues are inevitable, it doesn't mean they're unconquerable.
Here is a list of things you can do to help you solve your issue and move on in your relationship:
See the issue as an opportunity
Having challenges and disagreements in a relationship are actually positive. They give you and your partner an opportunity to grow as individuals and as a couple. Recognize your issue as the potential for positivity.
Determine if it's a deal breaker
How grave is the issue really? There are some fundamental issues that may inherent of your partner and are hefty enough to be considered deal breakers. However, the majority of issues are not crucial enough to lose all of the fantastic parts of your relationship. If the issue you're dealing with is not one of those essentials, choose to work it out instead of corrupting your relationship over it.
Choose your battles
If the issue is not a deal breaker, evaluate its importance overall. In the course of your relationship, there are a multitude of things that you and your partner will not agree on. You can't win every battle and you can't even fight every battle that comes your way. Assess the problem and decide if it's one of the fights that's worth fighting.
That little affectionate touch can do a lot to keep the two of you speaking civilly. It's shockingly hard to speak angrily to someone who you are holding hands with.
Intense issues have a habit of coming up late at night when you're finally alone, but this isn't necessarily the best time to discuss your deep-seeded issues. Take a beat (like a good night's sleep) before having these discussions so your emotions don't run the show. Sometimes sleep can offer a much needed perspective.
Remember that your partner is not you and that's part of what is so great about him or her. A relationship is built of two people with different talents and abilities as well as opinions and desires. Recognize their individuality as a positive thing and not something you should change.
Schedule an appointment
It can be helpful to set aside a time to discuss the issue. Doing this can prevent you from bringing it up at a time when you're both tired or when you're in a setting that is inappropriate for the discussion. Furthermore, it allows both of you to rationally ponder your own points of view, maybe even preparing beforehand a list to guide the discussion. Scheduling an appointment to discuss the issue can foster an environment where you can work the problem out.
Try to understand your partner
This should go without saying, but never allow yourself to have tunnel vision of your own perspective. Always seek to understand what your partner wants specifically and why that is. This can help you either change your own views on the matter or at least help you be considerate in making compromises or asserting your own beliefs.
Use "I" messages
Throwing fiery balls of "you" at your partner makes them feel attacked and prevents progress toward solutions. Instead, express how you feel by say things such as "I feel..."
Agree to disagree
Evaluate the issue and decide if it's necessary for you to resolve it. Some issues are better left alone. Decide if your problem is one that you can just decide to move past.
Pause before responding
Just taking a breath to get your bearings can prevent you from speaking emotionally and saying things that you don't actually mean.
In every relationship, sacrifices must be made. When joining two different people, it's inescapable. The key is learning to create compromises that don't consistently cause one partner to sacrifice more than the other. Get creative and evaluate several different ways the two of you can each get some of what you want to find the best compromise for the both of you.
It feels great to be right and not so great to be not so right. Allow yourself to be wrong sometimes. It's okay. Be humble enough to accept that you make mistakes and aren't right all the time; it's part of being human.
At the end of the day, you may need to call in some back up. An objective third-party may give you the perspective both of you need to solve your issue or be able to offer you tactics and problem-solving skills unique to your situation.