Kapalabhati means shining skull. Don’t worry: this doesn’t mean you will go bald performing the practice. There are two very different definitions of kapalabhati in the ancient texts. The Gheranda Samhita states that kapalabhati is one of the six cleanses,  and thus is not a pranayama. In the Hatha Yoga Pradipika, kapalabhati is a breath exercise similar to bhastrika. This is the version we will look at.
Normally when we inhale, the diaphragm is active and lower than its resting position – we use muscular effort to draw in the breath. Exhaling is a passive relaxation of the diaphragm, which rises back to its shortened position just under the lungs, forcing air out. In kapalabhati this is all reversed; we actively exhale, and the rebounding effect results in a passive inhalation.
To do kapalabhati requires the stomach to be extended at the top of the inhalation, and drawn in at the end of the exhalation. This is not easy for many people. When we are born, our natural breathing rhythm is like this: watch a baby breathing while lying on her back – her belly rises on inhalation and lowers on exhalation. This natural movement is very healthy; each breath brings the diaphragm down onto the liver and stomach, compressing the abdominal organs. Each breath is a healthy massage. Unfortunately, almost one half of all people lose this natural breathing action and either reverse the movement of the stomach, or don’t move the stomach at all when they breathe – instead, they move only the ribs (which is a much shallower movement). This deprives the organs of a regular massage sessions, and also restricts the amount of air that is drawn into the lungs.
If you are a belly breather, kapalabhati will be easy to start. If you are not, you will struggle with this practice. In either case, a beginner will find this much easier if she places one hand on her belly as she breathes. Focus on making a sharp inward movement with each exhalation. After the exhalation, relax the stomach and allow a passive intake of breath to happen. Go slowly until you can find a smooth rhythm. Sharply exhale through the nose, as if you had a mosquito stuck in there and you want to blow it out. Relax all your other muscles. Often beginners will contract and contort their whole body trying to get this exercise. You do not need to clench the facial muscles or jerk the torso; slow down and be more deliberate.
Do about thirty breaths, finish with a deep inhalation, and then exhale completely, bowing forward, squeezing the navel to the spine. Retain the breath on empty lungs, and straighten the body, engaging all three bandhas, performing the maha bandha. Bring your awareness to the muladhara chakra, the perineum. With lungs empty, you will not be able to retain the breath as long as when the lungs are full. Don’t worry about it. When you need to breathe, breathe. If you have to gasp as you release, you are holding too long. After releasing, sit quietly and watch the energy inside. If you feel able, repeat this two more times.