I've begun here with yogic three-part breathing, or Dirgha Pranayama. This pranayama teaches you to get the most out of your breath. When people try to take in a lot of air, they tend to gulp it in and rapidly expand the ribcage. This doesn't actually take in much more air and can lead to injuries (and you really don't want to have to tell people you injured yourself breathing!). Dirgha Pranayama will teach you to take in the most air without compromising your body. In the interest of time, in the video I teach the breath as 1)chest breathing, 2)thoracic breathing, and 3)diaphragmatic breathing. When I do this with students I would then reverse it, and try to have them breathe first to the belly, then the ribs, then the chest before integrating them all. In the video we don't reverse it, just integrate, so if you feel it would be helpful you can reverse the order before the integration. I begin with very shallow chest breathing, and every time I do this pranayama in class someone mentions that this is how they breathe naturally. Doing the three-part breath will help you to avoid that. Once you realize how revitalizing it is to take deep healthy breaths, you won't want to breathe shallowly ever again.
The second pranayama in the video is Ujjayi Pranayama, or Victorious Breath. It is a bit more advanced than the three-part breath and may take some time to master. Be patient. Once you have the Ujjayi Pranayama down you can perform it while doing yoga poses. The main indication that you are doing it right is the "ocean sound." Your breath should be loud and sound almost exactly like the ocean waves. Doing this breath at the beach in time with the ocean is an amazing meditative experience that I recommend.