Svadhyaya the fourth of five niyamas is the "study of one's self."
In Living the Yamas and Niyamas by Aadil Palkhivala, he writes:
"As yoga teachers, it's our responsibility to help students develop a practice of constant inner reflection so that they will become aware of the changes that yoga is making. This can be done by asking such questions as, "Why are you here? If you had all the money, all the time, all the energy you wanted, what would you do with your life?" In my teaching, I find that these sorts of questions stimulate the practice of svadhyaya"
When we first begin a yoga practice, there are many overwhelming and potentially confusing new concepts, i.e. "you want me to put my foot where?" and "why are we chanting om?" After a few classes, as we begin to get more comfortable with our teachers and begin to enjoy the after-effects of practice, we may begin to notice a new sense of ourselves that we'd never experienced prior. The sense that we feel more alive, or that we have musculature that we never even knew about. This turning inward and observing your personal growth is the essence of the fourth niyama. You can even begin your classes by asking yourself, "what did I come here to achieve?" And, any answer is the right one for you today, even if it is six-pack abs or peace of mind. They are all just stepping stones along the path.
In terms of your asana practice, svadhyaya is the part of the practice in which you tune in to what you are feeling. From the observation deck of the mind, you begin practice by sensing--how does your breath feel as you embark upon your practice? What bodily sensations are you experiencing? What is your mental state?
Observe, non-judgmentally, the state of your being prior to practice. And then you continuously check in as you progress. After each pose, come back to your observation tower and have a look. Have you been able to increase the flow of prana? Is your breath calm, steady and deep? Is the body becoming more supple, or are you holding tension? How about your mind? Are you making grocery lists and envying your neighbor's bakasana or can you quiet the ticker tape of the mind and tune into your practice?
In terms of your day-to-day life practice, svadhyaya is put into practice by watching your emotional states. Especially those that are uncomfortable such as anger, shame or sadness. Was it an external force that created your emotional state? If so, in the future, rather than jumping to an increased emotional state, can you begin to step back and observe the situation, observe the activity of the mind before your reactive sense of self (EGO) flies off the handle?
This capability is years in the making—and isn't easy. But the more often you come to the mat and come to the cushion, the more you can "study the self" to be able to soothe your potential reactive mind before it even starts.
This practice of yoga is all about self-transformation—the possibility of waking up to experience the joy of the real you. So quite naturally, you have to take a darn good look at yourself, spend some time with your svadhyaya practice, before you can begin to make true, effective progress.