Learning breathing techniques for relaxation and stress reduction takes practice. Unlike tranquilizing drugs, which often are effective when you first take them but lose their power over time, the effects of breathing exercises are subtle at first but gain power the more you repeat them. At first, some people do become light-headed, but you will find that this passes in time. I recommend that you continue with the breathing exercises, but try not to breathe as deeply or as intensely as you may have when you experienced the lightheadedness. Experiment until you find a level at which the lightheadedness doesn't occur and gradually work up from there.
If you're learning Exercise: 4-7-8, in which you count to four while you inhale through the nose, hold your breath for a count of seven and exhale for a count of eight, I recommend that you practice at least twice a day but that you don't do more than four breaths at one time for the first month. Then, if it feels comfortable, you can increase to eight. In time, you should notice a shift in consciousness after doing the exercise: a feeling of detachment, lightness or dreaminess - this is a sign that you are affecting your involuntary nervous system and neutralizing stress. Once you develop the technique by practicing it daily, it will be a useful tool that you can rely on when something upsetting happens, to dispel tension, or to help you fall asleep.
Keep in mind that when you breathe deeply, you want to let your abdomen expand. This is abdominal or diaphragmatic breathing as opposed to breathing with the chest. Abdominal breathing allows one to breathe fully, using total lung capacity, whereas chest breathing puts more of a strain on the accessory muscles of the neck and ribs, and limits lung capacity. Shallow breaths of high intensity may be the cause of your lightheadedness.
Don't give up on learning the techniques because of the temporary symptoms you've experienced. With some patience and practice, everyone can benefit from breathing exercises.
Andrew Weil, M.D.