how to aware of Dukkha ( "suffering", "anxiety", "stress", or "unsatisfactoriness")

To become aware of dukkha requires nothing more than watching yourself. This is a beginning step of a meditative practice. When we watch our own minds we will grow into awareness of experiences, and eventually the patterns that create each of those aspects of experience.

I only faced dukkha head-on after exhausting myself from ways of trying to escape it. I didn't know that that's what I was doing at the time. But until I had reached a certain point of exhaustion, I had no interest in a religion or philosophy that began with 'there is dukkha'. It seemed very wrong and like giving up.

It is one thing to be able to describe in words what it is, and another to become aware of your personal experience of it. It is the experience that is crucial.

What works for one person might not work for another. This is because there are various different shackles, things we believe are not dukkha but actually are. One person might have excellent understanding how one defilement brings dukkha while another person might be thoroughly wandering around in it thinking it is helpful. So different people will start with different levels of wisdom.

For people who can learn and understand from reading and who have a desire to meditate as a means of experiencing good states of being, descriptions of states of mind that cause dukkha are good starts. I am at a loss of sources to link however. If you have a background in other religions, lists of things like commandments, sins, holy laws, etc. when accurate, will all discuss various aspects of dukkha. In Buddhism and Hinduism there is a study of karma which can be meditated upon, to be understood, ultimately with the thought of being able to escape it.

In Zen Buddhism, there are often phrases or stories that when fully understood, are attempts at getting a person to break free from an unwholesome state of mind or an incorrect understanding.

Many religions will simply teach only the wholesome qualities to grow. This does not teach dukkha so much as it expounds on lessening it, which at the end of it all, is truly the only reason one is actually trying to understand what dukkha really is.

To become aware of and learn what dukkha is though, is to fully expose yourself to it such that you can fully abandon. A method of spiritual practice that focuses on only positive can often leave corners of the mind wondering a niggling thought. Temptation may still exist, even through a very long time of avoiding it. A meditative practice where you intentionally watch and expose yourself to all the dukkha of all your thoughts, is ultimately trying to get you to have not even a single underlying desire to follow any temptations that will increase your own dukkha because you will simply not be tempted anymore.

Now I could be wrong about this as I do not have exposure to these practices, but from hints and words of the sort of Buddhism practiced in Tibet, students will intentionally expose themselves to all sorts of dukkha-inducing things as part of the practice itself, to basically exhaust yourself of it until you have no more desire as you see that it is actually a false route to freedom.

For regular lay people, you don't need to do any of the above. So long as you are determined in your practice, you will naturally be inclined to do all those things you want to do until exhaustion anyways. Furthermore, there will naturally be exposures left right and center all the time. BUT this can result in lots of spreading of dukkha however, as we generally will influence others in our fumbling towards the correct way of being. A meditative practice internalizes these fumblings. For instance, I went through a divorce and another breakup to learn that sensual love and passion, not just lust, was actually holding me back. This caused lots of pain although I did actually learn.

However, the awareness is key still. All our actions naturally all the time are inclined to our escaping of suffering, but having skills to know what is good and what isn't is necessary for growth. Bringing in awareness into daily life is necessary. We grow our awareness from things like taking time to just sit and watch ourselves. Watching our own breathing or natural body rhythms (I eventually felt chakras) is important, especially if you are going down a contemplative, meditative path for approaching your awareness of dukkha. All it takes is a moment of 'ah, I am here and watching' which shares similarities to what you would do if you are interested in lucid dreaming, simple checks throughout the day.

Of course the purpose of the awareness is to check yourself, wisely noting your mind, emotions, etc. so as to act appropriately, not just become aware. There is an ultimate reason for the growth of awareness, to learn what dukkha is so that you can leave it behind for good, forever.

[Ven. Sariputta:] "Now what, friends, is the noble truth of stress? Birth is stressful, aging is stressful, death is stressful; sorrow, lamentation, pain, distress, & despair are stressful; association with the unbeloved is stressful; separation from the loved is stressful; not getting what is wanted is stressful. In short, the five clinging-aggregates are stressful.

https://www.accesstoinsight.org/ptf/dhamma/sacca/sacca1/dukkha.html

Dukkha is a state in which our expectations differ from the actual state of the world; it's often tied in with a perverse sense of permanence. For instance, it's fairly common for people to assume that their favorite sports team are 'winners'. That produces dukkha when the team loses (because losing violates expectations), and it produces dukkha when the team wins (because winning amplifies the expectation that the team will always win).

Tanhā is a stubborn demand that our expectations must become real; it's usually translated as 'craving,' but... We often see that in super-fans, for instance, who somehow have become so attached to the fortunes of their team that much of their emotional life revolves around it.

All we need to do to be aware of dukkha is to notice when we are discontent with the way things are. If we feel a sour/angry/pissy/grumpy/churlish attitude rising, it's because (somewhere in our head) we expected A from the world and got B. If we feel a pleased/smug/superior/sanctimonious attitude rising, it's because the world momentarily aligned with our expectations, and we damned well think it should do it more often. Tanhā is a bit more difficult to recognize because tanhā usually involves a a self-righteous sense that our expectations are 'real' and the actual state of the world is 'false'; we are so committed to the way things should be that we lose connection to the world as-it-is entirely.

Ridding ourselves of dukkha is advanced practice; it's extraordinarily difficult to live without expectations, and I'm not certain it's realistic or healthy outside of monastic life. Ridding ourselves of tanhā is valid and valuable for all of us, though.