In classical Yoga, prāṇāyāma means controlling the breathing process. Here, prāṇāyāma means prāṇa = motility or that which enables life + yama = control. So, prāṇāyāma is actually control of motility (prāṇa) using breath as a tool. Prāṇāyāma is a natural progression of āsana. Consequently, the various techniques of prāṇāyāma are generally taught with āsana. School of Yoga considers proper practice of prāṇāyāma to be as important as practice of āsana.
The Hatha Yoga Pradeepika has a complete chapter on prāṇāyāma.
This section of School of Yoga addresses all major aspects of prāṇāyāma.