Pranayama by Baba Ramdev
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 :)

English speakers: YouTube Playlist of Pranayama Videos in English is available. The instructions in Hindi videos are more spiritual and vivid (how to breathe, what to think, where to focus, what benefits to expect).

Personal Notes: 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.

Physical: 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.

Details: YogaPoint article on Kapalbhati.

Part 3: Baharya (6:39)

Duration: Three to five times. With practice, max 11 times. Experts may do it for 21 times.

Physical: Requires three bandhas: Jalandhar Bandha, Uddiyana Bandha and Mool Bandha.

Details: YogaPoint article on Tribandha.

Part 4: Anulom Vilom (9:34)

Duration: At least ten minutes.

Physical: While inhaling, don't fill stomach. Inhale only till diaphragm. Do this pranayama very patiently. Don't hurry.

Mental: Slowly, with joy and relaxation. Remember 'Omkar' when doing the pranayama.

Details: YogaPoint articles: Anulom-Vilom IAnulom-Vilom II

Part 5: Bhramari (9:00)

Duration: As long as you feel like.

Physical: Many details related to hand position. For example, how to close the ears, where to position fingers, and so on. See video.

Mental: Remember divinity. Repetition of 'om' is said to be magical. Many saints are said to have experienced oneness through repeated chanting of 'om'.

Details: YogaPoint article on Bhramari

Part 6: Udgeet (9:11)

Duration: As long as you feel like.

Physical: Repitition of 'om' is magical.

Mental: Feeling of submission to higher power.

Part 7: Ujjayi (7:52)
Details: YogaPoint article on Ujjayi.
Books and Articles

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.

The Science of Pranayama by Sri Swami Sivananda (First Edition in 1935, Freely available on the web since 2000).

High quality articles are available at Yoga Vidya Dham (Nasik, India) Website.

Teachers in Silicon Valley

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.

Art of Living Foundation (AoL) by Sri Sri Ravi Shankar runs stress reduction programs worldwide. The main technique taught in the introductory AoL course is Sudarshan Kriya, which is a sequence of Pranayamas to be practiced about 30 minutes every day.

Sivananda Yoga Farm in Grass Valley is nearby. Yoga and Pranayama in Sivananda style is taught here. There is a retreat every weekend.

Mt Madonna in Watsonville was established in early 1970s by Baba Hari Dass. The center teaches according to the 8-step Ashtanga Yoga as outlined by Patanjali — Pranayama is the fourth limb out of eight.

Vasanthi Bhat teaches Yoga, Pranayama and Meditation in San Jose. She has been teaching for 25+ years.