The practice of tapas is one of the five niyamas, or moral codes in Patanjali's Yoga Sutras. In Sanskrit, the word tap means "to burn", which lends itself to the idea of tapas being a fiery passion and intense, focused self-discipline within the yoga student. It is the idea that the yogi will identify attainable goals and joyfully do what is necessary to achieve them.
There is a fine line to all of this, however. For instance, many people who practice yoga prefer to alter their diet for various reasons (health, the environment, animal rights, etc). Consider the difference between the discipline of someone who alters their diet with the sole goal to be a size xxs, versus one who changes their diet with the focus on health reasons. One is ego driven, and the other takes a more tapasic approach. Keep this distinction between ego and non-attachment in mind when practicing tapas.
In terms of the yoga practice itself, being extremely focused and disciplined does not mean perfecting the most advanced poses. Many times, when the goal is just to master difficult poses, the ego becomes attached to being known as "the advanced yoga student". The tapasic approach would be to identify (ego-free) goals that you fundamentally believe in- like maintaining a daily yoga practice. Remember the "difficult" poses will come, but they are not the ultimate goal. What matters most are the lessons learned through the journey of your practice.
While many equate self-discipline with deprivation, it can actually be nourishing and beneficial. For example, a yoga student practicing tapas may wake up early, eat well, abstain from drinking, practice meditation and yoga, and go to sleep early because the benefits far outweigh the results of "the norm".
For my practice of tapas, I've been focusing on getting healthy after about six weeks of bronchitis. I've been juicing daily (post about that coming soon), experimenting in the kitchen with healthy ingredients, started going to the gym again, and started teaching yoga after four weeks off. What are your current goals? And how will you achieve them with a tapasic approach?