Meditation and Yoga are very diverse subjects to have a lot of detailed discussions on breath control, awareness, and techniques. While it is not possible to tell you which method is the correct method to observe breath, as what is correct for you, might not be correct for the others. Drawing of breath on various parts of the body is one of the common methods in Kundalini Yoga and Kriya Yoga (the latter is a more efficient method for the former usually).
In Samkhya interpretation, one static aspect (or masculine) is usually denoted with prakriti and the other force (also called life-force) as prana - the force that animates the Prakriti (for example - body and soul).
It is important to note that breath is not itself a prana, but rather it is a carrier of prana that is used to activate various modes (also called Nadis ) in the subtile body.
In Kriya Yoga, different practices of breathing and different forms of breathing are taught to the students for different purposes - relaxation, calmness, cultivating humility, etc depending on what Nadis are activated.
In general, too much inward breath should be avoided as it might arouse of Kundalini Life force - when uncontrolled without any guru or third person by your side at the moment might land one in the hospital. A gentle drawing of prana from the chest and mind is recommended as a preparation for any other meditation. In case you are unsure about the technique, one can just focus on breathing on the nostrils - which is a very good general method accepted in both Hinduism as well as Buddhism.
These subjects are often under pranayama yoga where the whole purpose is to control the prana for various purposes.
- Vivekananda, Swami. Raja Yoga (Annotated Edition). Jazzybee Verlag, 2012.
- Nadis are branching points (or petals) of chakra. The exact number of Nadis differs from school to school and scripture to scripture. Usually 72,000, but the number 108 most important ones are accepted by both Hindus and Buddhists.