It sometimes helps to break the principle of dependent origination down into the sequence of events that happen whenever there is contact with something.
When there is contact with an object of the senses, this is the sequence: form/matter: this is what is seen, the form both of the object seen and the seer of it. This creates a sensation or a feeling, either pleasant, unpleasant or neutral. This leads to apperception, which is recognizing or not-recognizing the form that is seen (for example naming it). Then habit kicks in (I like those, I want one of those, it's been some time since I had that). This gives rise to ideas about the thing, one's knowledge of it, how one 'relates' to it, and so on.
The point is, that these sequences are happening in quick succession, all day long, without much awareness of what is going on. In other words one is caught up in reactions to what is seen, what is heard, and so on, reacting to it, judging it, wanting or disliking it. This leads to habituation, which leads to clinging, which leads to suffering when what is clung to is lost, or when it is not satisfying, and so on.
Of course it goes in to much more depth and detail, but that level of analysis might be useful in understanding how the principle applies in daily life.