Basically, the understanding of Kamma begins with objective awareness. I talked about this in the answer to an earlier question today. By being able to note the hindrances when they are present and getting to that objective awareness so we are not either liking or disliking, we have non-judgmental objective awareness. Then, we can look into the Law of Cause and Effect. This is investigating Kamma moment-to-moment: if you think this way, then this is the result. On the other hand, if you have unselfish emotions, then pleasure or the fading away of Dukkha is the result. By looking into this Law of Cause and Effect moment-to-moment in the mind, we develop an understanding of Kamma.
Then we're encouraged by the Buddha to universalize this understanding. When he talks about the Five Daily Recollections, he says, "Not only me, but all beings are owners of their Kamma, heirs to their Kamma." We're also encouraged to develop our experiential understanding of this Law of Cause and Effect with the Seven Factors of Enlightenment in the Fourth Foundation of Mindfulness; to look into the causes of the Factors of Enlightenment so that we can understand that it's an impersonal law, this impersonal Law of Cause and Effect. Looking into the Law of Cause and Effect is basically practicing the Fourth Foundation of Mindfulness.
Regarding Dependent Origination, it also depends on the experiential understanding of seeing. When we react to the sense contacts, we react to the feeling that arises from the sense contact: pleasant, unpleasant, neutral. This is investigating into the Five Aggregates, basically, or the problems that arise dependent on the sense doors. That is, we have to develop a strong awareness of our sense doors to understand how Dukkha comes to be. Usually it's coming from our reaction to the pleasant, unpleasant or neutral feeling. We grab it, we make it mine, and there is birth of "me" and "mine." Rather than it just being a pleasant, unpleasant or neutral feeling arising and passing, we have made it into "mine," and then comes all the Dukkha from this.
Using Wise Reflection, we also understand that when you have a future thought, what are you wanting? Normally, when the craving is present, you're wanting to experience pleasure. Where does that pleasure come from? Usually, it comes from the six senses, so then you can contemplate how the six senses depend on the body, which depends on birth, and because of birth there is death, sorrow, lamentation, pain, grief and despair. This is using the wise contemplation type of meditation to understand this process more deeply. What you can do to get an experiential understanding of that is to contemplate in this way anytime there is desire in the mind. You can ask yourself what are you wanting?
Use the sense doors and ask what pleasant feeling are you wanting from what sense door. And you can ask yourself, if I have these sense doors now, in order to get this future contact that I am wanting, what do I need? What do I have to become in the future? I have to be born again in the future. That's basically in this present life. That's what's happening. The pleasure for the future causes us to wish to be born in the future. And because we wish to be born, we need this body, which means the birth of this body and the birth of this mind. From the birth of this comes not just pleasure, but also pain; not just gain, but also loss; not just fame, but also obscurity; not just praise, but also blame; and also sorrow, lamentation, pain, grief and despair.