Pranava yoga

Pranava yoga is the classical method of meditation outlined in the Upanishads, the Bhagavad Gita, and the Patanjali Yoga Sutras. It is also called Om yoga and Om yoga meditation. It is, simply put, fixing the mind on the sound of the mantra “Aum” – the sacred syllable that both symbolizes and embodies Brahman, the Absolute Reality – as the mantra is constantly repeated in unison with the breath. The purpose of pranava yoga is to become free from suffering and limitation.

The purpose is well stated in the Upanishads:

“What world does he who meditates on Aum until the end of his life, win by That? If he meditates on the Supreme Being with the syllable Aum, he becomes one with the Light, he is led to the world of Brahman [the Absolute Being] Who is higher than the highest life, That Which is tranquil, unaging, immortal, fearless, and supreme.”

– Prashna Upanishad 5:1,5,7

Bhagavad Gita
Speaking from the perspective of the Infinite Being, enumerating his major manifestation-embodiments, Krishna says: "I am the syllable Om."(Gita 7:8) He also says the same thing in 9:17 ("I am...the sacred monosyllable") and 10:25 ("Among words I am the monosyllable Om").
What to "do" with aum is then outlined by Krishna:

"Engaged in the practice of concentration... uttering the monosyllable Om--the Brahman--remembering Me always, he...attains to the supreme goal. I am easily attainable by that ever-steadfast Yogi who constantly and daily remembers Me."

– Bhagavad Gita 6:13; 8:12-14

Patanjali’s Yoga Sutras
"Ishwara [God] is a particular Purusha [Spirit, Person] Who is untouched by the afflictions of life, actions, and the results and impressions produced by these actions. In Him is the highest limit of omniscience. Being unconditioned by time He is teacher even of the ancients. His designator [vachaka] is the Pranava [Om]. Its japa [constant repetition] and bhavanam is the way [or: should be done]. From it result [come] the disappearance of obstacles and the turning inward of consciousness. Disease, languor, doubt, carelessness, laziness, worldly-mindedness, delusion, non-achievement of a stage, instability, these cause the distraction of the mind and they are the obstacles. [Mental] pain, despair, nervousness, and agitation are the symptoms of a distracted condition of mind. For removing these obstacles [there should be] the constant practice of the one principle [the japa and bhavanam of Om]."

– Yoga Sutras of Patanjali 1:24-32

Modern schools of Yoga
Aerial yoga
Anahata Yoga
Ananda Marga
Anusara Yoga
Ashtanga Vinyasa Yoga
Bikram Yoga/ Hot Yoga
Cardiac yoga
Chair Yoga