That's what we're doing. In order to investigate into our own Dukkha, one has to first become aware, start to investigate into our own body and mind. That's the basic practice: trying to become aware of our body so that we become aware also of our thoughts. As well, to become aware of the results of our thoughts, becoming aware of the hindrances, becoming aware of the results of feeding the hindrances, seeing the Dukkha that arises and understanding the Law of Cause and Effect. As we begin to understand this basic idea of cause and effect, we start to transform a lot of our ideas about where Dukkha really comes from. People normally believe that their suffering comes from external conditions, but as we investigate into our reactions and the results of our reactions we start to see that a lot of it comes from our ignorant reactions and our wrong views about ourselves.
As we become more aware of our bodies, we start to understand impermanence more clearly, how everything arises and passes. We understand the result of clinging to impermanent things: it brings suffering. Investigating into the hindrances helps us to understand the Law of Cause and Effect, and helps us use analytical meditation much more effectively because we have some experiential practice about understanding Dukkha and the cause of it.
Another way to investigate into Dukkha and the cause of it, once we have this basic understanding, is to use various types of reflection-type meditations. Of course we do Compassion/Lovingkindness to see how our selfish emotions cause Dukkha for ourselves and that by developing unselfish emotions we start to see the other side. Developing unselfish emotions such as Compassion/Lovingkindness bring about the causes within ourselves for the ending of Dukkha. There are many other reflections which will help us understand the first two Noble Truths and hopefully also the last two.