"If we examine moments of joy and peace we will discover that what they offer are veiled, fleeting glimpses of the Self. They are the instances when the mind, through a combination of factors (primarily suspension of craving) has momentarily become steadier, enabling it to reflect a hint of the peace within."
There are two very important words in Yoga: Prana and Vrittis. Prana is the universal life force, while Vrittis is the incessant, fluctuating movement of the mind. In Yoga we manipulate the Prana in our bodies with the practice of asana and pranayama. Pranayama is essentially the practice of regulating the breathing process. Here is where the two words come together: mind and breath are directly related. When the mind is calm, so is the breath; when the breath becomes agitated the mind follows. When we control the breathing process, the mind becomes clear and calm.
Ujayi pranayama is a safe pranayama technique ('ujayi' in sanskrit means to conquer) usually translated into victorious breath. In Ashtanga Vinyasa we use Ujayi pranayama to count our vinyasas, smooth and slow down our breath, therefore quieting the mind, overtime 'conquering the vrittis'. The quality of our breath mirrors our state of being, so when we practice we look to create a better state for ourselves to be in, we quieten the unwanted mind stuff, peeling away layers to let The true Self, or Atman, shine through. The Atman, lives in a state of peace, it is the vrittis, that the conscious and subconscious mind create, that enable us to feel with clarity this state of tranquility .If we let the mind run on its own we cannot perceive pleasure, in order for the inner joy to shine through the mind must be controlled, therefore the breath must be steady. An ideal practice is that were the mind is vacant, or fixed on the void. Only in this void space can we find tranquility, happiness and joy, which is the state we are born with, before the vrittis. All feelings, all emotions, whatever state we find ourselves in, is part of us, there is nothing to be fixed about that, it is the way we react to it, the vrittis, mind stuff that we attach to it, that creates suffering, and veils the real never changing state of the Self: a state of peace. When we practice Ujayi pranayama the veils covering the Self become transparent, then the fullness of the Self shine forth.
Ujayi pranayama is the most accessible form of pranayama, an experienced teacher may guide you through other practices, a good practice that you may want to consider is this:
as you breath meditate on the breath
with each inhalation meditate on the state of fullness, on its sensation
with each exhalation meditate on the state of emptiness, on its sensation
meditate on the transition between emptiness and fullness, observe, as audience, the reactions the mind has to these moments, without attaching to its reactions, just watching and letting it pass.
For more reading on the topic of Vrittis and Pranayama:
Yoga Sutras 1.2, 1.33&1.34 , 2.49