Ashtanga yoga uses a special type of yoga breathing exercise called Ujjayi Breathing. In this method of breathing you have to constrict the back of your throat just above the point where you swallow. This narrows down the passageway through which you breath, meaning that the muscles that you breathe with have to do more work both while you inhale and while you exhale.
The narrower you make your throat passage the more your respiratory muscles have to work. The more open you make this passage the less your respiratory muscles have to work.
The advantage of this is that it exercises your respiratory muscles. Since your respiratory muscles are working harder, this generates heat. This type of breathing also creates a deep hissing sound. The hissing sound is in part due to the restriction of the throat, and also in part because of the tension enduced in the respiratory muscles which can make the thorax act like the sounding box of an instrument. (That's my explanation anyway.)
Ideally you can vary the size of your throat passage and the work that your respiratory muscles do so that you can vary the volume of this sound.
Why try to create a sound when you breathe? To give you something to focus on. You can tune in to your breath by listening to the sound of your breath. And if you are really paying attention you can notice if you stop breathing or if your breathing becomes too quick.
While using ujjayi breathing you can work at holding your lower belly in while you inhale. At the same time let your ribs lift and expand and allow your upper belly to expand also. While exhaling, slowly and smoothly let your ribs sink down. You can release your belly at the same time.
By holding your lower belly inwards while you inhale you are activating the lower fibers of your transverse abdominus. This muscle is made up of fibers that run horizontally around your belly between your pelvis and your ribcage.
By the way, the lower belly in this case is the portion of your belly about four to five finger widths up from your pubic bone.
If you upper belly expands while you inhale then that is the result of your Respiratory Diaphragm contracting and pressing downwards on the contents of your abdomen. The diaphragm also helps your ribcage to lift.
The intercostals are the muscles between each set of ribs. These muscles act on the ribs to cause the ribcage to expand or contract. When inhaling they help your ribcage to expand.
When you exhale you can either force your exhale using your intercostals and your abs, or you can relax and allow the weight of your ribs sinking down cause your exhale for you.
When doing Ujjayi breathing your inhale and exhale through your nose.
If you aren't used to breathing through your nose, try inhaling through your nose and exhaling through your mouth. Then try inhaling and exhaling through your nose for once breath cycle and then exhale through your mouth on the next breath cycle.
To make breathing through your nose easier you can try spreading your nostrils by using the muscles at the side of your nose. You may find it helpful to lift (or activate) your cheeks. (The cheeks on your face of course!)
Once you are used to breathing through your nose, practice narrowing your throat. See if you can vary the amount your narrow your throat and see if you can notice the difference it makes in your "respiratory effort." Notice the sound that accompanies the narrowing of your throat.
Next try to hold your lower belly in while you breath. You can hold it in for your inhales and let it go while exhaling. Or you can also try holding it in while you inhale and exhale. Notice how both options feel. Again, notice how you feel and the sounds that accomany any changes that you make.
The next step is to try ujjayi breathing while you are actually doing yoga poses. Remember that you can always vary the size of the openening in your throat to make your breathing easier or harder depending on the ease of the yoga posture that you are doing.