When couples come to me for relationship counseling, I start the process by asking what are the couple's goals in working with me. The most frequent response to this question is "we'd like to improve our communication". What this actually boils down to the majority of the time is that each partner would like to be better heard and understood. It's frustrating and upsetting if you feel your partner isn't listening or doesn't "get" you, and serious fights, or a permanent rupture, can develop out of that frustration and upset.
There can be several factors contributing to the feeling of not being heard or understood. A very common one is "Oh, here he/she goes again:" assuming that we know what our partner is going to say beforehand and therefore tuning out. Most of us are adept at reading whether or not someone is paying attention to us, and can quickly pick up on a partner's inattention. So make an effort to listen without assuming you know what your partner is about to say.
A second is related to the "fight or flight" emotion sometimes involved in the communications process. Often communication involves some form of complaint (e.g. "I wish you would...." or "I wish you wouldn't....."; You always..." "You never....."). Some people are exceptionally sensitive to criticism, and even a relatively subtle complaint will be viewed as an attack and trigger defensiveness. Good communication simply can't occur when one of the parties is being defensive, since the person feeling criticized is busy formulating counter arguments or figuring out how to exit the situation, rather than truly listening. Pay close attention to your style of criticizing or complaining, and to the degree possible request a change in your partner's behavior rather than attacking it (e.g. "It would mean a lot to me if you....." rather than "I hate it when you....").
Relatedly, examine your own behavior for the opportunity to improve communication rather than blaming your partner. A very typical complaint is "When you.......I........", for example "When you are late it makes me feel undervalued," or "When you have that look on your face I feel resentful." Remember that in actuality no one can make you feel a certain way - when you feel that someone is making you feel a certain way, recognize that you are experiencing a conditioned response (akin to Pavlov's dogs salivating at the sound of a bell). Unlike Pavlov's dogs, however, humans have the ability to examine their behavior. It's not easy, but try to take responsibility for your feelings, rather than blaming your partner for them, and practice alternative ways of responding.
Another communications problem is over or under explaining. Some people's communication style is to be very detailed, others prefer to speak in a kind of shorthand. Excessive detail can bore your partner, while excessive brevity can result in miscommunication. This is a particularly difficult issue, as our explanatory styles are acquired over many years, and they are as engrained as posture or as facial expression. But with focused attention it is possible to alter the detail with which we describe situations or problems.
Finally, the tone of the couple's communication is critical. Avoid nagging, put-downs, and derision, and above all avoid indications of contempt or disgust. Even if there is validity to the complaining partner's point, speaking from one of the aforementioned places is sure to shut down communication, and will actually engender increased hostility.
Gaining an awareness of the problems outlined above is hard or even next to impossible, as communication patterns become engrained fairly quickly and become almost invisible over time. Relationship counseling provides a setting in which patterns can be observed with a fresh, objective perspective, and appropriate solutions can be formulated and practiced.