Baba Ramdev (born 1974) is an iconic figure in India who has rejuvenated interest in Yoga and Pranayama among the Indian masses. In the videos below, Baba Ramdev gives extensive instructions in 'shuddha Hindi', which is music to my ears :)
Below each video, I have jotted down brief personal notes for myself. I have not transcribed all sentences in the video. You should watch these videos yourself and make your own notes, especially if you have health problems. Baba Ramdev actually gives lots of instructions. I've found it difficult to remember them all. So I watch these videos every few weeks. Every time, I learn something new.
Western Research: See Wikipedia article for some references. It appears that there is far more research on meditation than on pranayama.
Part 1: Bhastrika (9:58)
Duration: Two to five minutes. Don't do beyond five minutes. Take rest when tired, then restart.
Fill air only till diaphragm, not into stomach.
Deep in-breaths, quick out-breaths.
No tension on face.
Mental: This pranayama must be done with relaxation, at ease, remembering purity, energy. Be happy and joyful. Imagine that all energies in the universe are in my mind, heart, body. Do the pranayama with dedication, joy, focus. Imagine that I'm getting stronger, that my aura is getting stronger.
Part 2: Kapalbhati (9:47)
Duration: Minimum of 5 minutes. Maximum of 10 minutes. Beginners should do this thirty times. Then take rest and restart.
Physical: Full effort is to be invested in exhalation - our only thought should be to get the breath out completely. Inhalation is autonomous. Exhalation is similar to vomiting or when we clean our nose.
Mental: 'Kapal' denotes forehead and 'bhati' denotes 'deepti' or 'oj' or aura. Imagine that all toxins of our body are going out with each exhalation. Baba Ramdev says that Kapalbhati Pranayama is very special. He equates this Pranayama to 'sanjeevni', a magical Indian herb with extraordinary properties.
The classic reference for Pranayama is Chapter II of Hatha Yoga Pradipika, originally written in the 15th century AD. This text is terse and practically impossible to understand without interpretation by a teacher. Many commentaries have been written over the ages.
The best-known modern reference for Pranayama is The Light On Pranayama: The Yogic Art of Breathing (294 pages, 1985) by B K S Iyengar (born 1918). The book emphasizes that Pranayama can be dangerous -- it must be done under the guidance of an experienced teacher, and only after one has sufficient practice with Yoga (which prepares the body for Pranayama). For inspiration, you may check out B K S Iyengar practicing in 1938 (silent films): Part I and Part II. And see him practicing in 1991.
Many good Iyengar Yoga studios are present all over the bay area. For example,there is California Yoga Center in Mountain View and Iyengar Yoga Institute of San Francisco. Many Iyengar Yoga teachers have been taught by Ramanand Patel, who is a disciple of B K S Iyengar and Dayanand Saraswati. Ramanand Patel is somebody special. He bridges the gap between the east and the west by speaking both languages.