Having determined that a duty exists between two people, an awful lot of litigation revolves around whether one person has breached that duty to the other.
What is involved is always a fact-sensitive inquiry. For example, say Percy and Darla are in a car accident at an intersection controlled by a traffic light. Both parties say, in my example, that the light was green for them when they were struck by the other car. Having established that both parties owe each other a duty of due care (i.e. not to crash at the intersection), the question is whether (if Percy sued Darla) Darla breached her duty by crashing into Percy. One way to show that would be to show that Darla ran a red light.