Breathing is one of the most basic as well as important aspects of meditation. Whatever technique you decide to use, breathing will most likely play a large part in it. For the most part, the average person breathes very shallow - drawing in air from the throat area as opposed to taking it in deeply from the chest. There is a difference to be aware of. In meditation, deep breathing is very important - to inhale, slowly expand your chest, aware of the air as it moves through you - exhale slowly and just as deliberately. Be sure that your breath is even and that you follow it with your focus. Just sit in the silence with that intention, simple and deliberate breathing. Starting with just a basic breathing meditation, be aware of your breath. For that moment in time that is the only thing that your mind should focus on -- the gentle inhale and exhale of your own breath.
You'll come across many excellent breathing techniques, go with what you are comfortable with and stick with it. To give you a good starting place, I've found this breathing method to be very, very beneficial and recommend it for anyone no matter what stage you are at in your meditative learning. It is as follows...
Place your tongue just behind the ridge behind your upper teeth, this works on an energy level, completing a main circuit where in energy flows through out the body (similar to the kundalini line) - hold that position through out this exercise. Next, inhale through your nose, counting slowly to four. Hold it, counting slowly to seven; then exhale slowly through your mouth, this time counting to eight. Note the operative word here is "slowly" - always be deliberate in any meditative exercise, it helps control and deepen your focus. This is a very simple but very powerful exercise - just remember: 4, 7, 8. Inhale 4, hold 7, and exhale 8. It acts on many physical and mental levels, it steadies the mind and centers the energies of the physical body. Try it several times in succession and you can automatically feel its effects.
Proper use of meditative breathing can begin to surface in the various aspects of your life. When you are comfortable with your breath (i.e., it has gone from its normal shallow to a much deeper state) you can call on it at different points in your day to day life. Various relationships, anxiety, stress, five o'clock traffic - you name it, through the use of this breath you can bring yourself back to your meditative center at any moment. *Highly* beneficial, especially if you're like most people and don't live in a peaceful monastery in the mountains. Just stop and breathe during your regular day - take two minutes and go through the basic exercise. Remember that meditation is not something that you do once or twice a day in special place in your home - it is to be integrated fully into your life as a whole. Whether you're at work or school - it's vitally important to take a few minutes just to center yourself and regroup. It's very easy just to get into the hectic flow of the day, but by bringing your meditation with you, you're able to transform that everyday life. Which is what many people strive for, transforming the day to day - it doesn't take a great awareness to do that, just a few minutes here and there to quiet yourself, be aware of where you are and simply breathe.